The percentage of the cookies were gingerbread is 60%.
Given that, the total number of gingerbread cookies and sugar cookies= 55 and the number of gingerbread =22.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%"
Here, Difference =55-22
=3
Percentage =33/55 ×100
= 0.6 ×10
= 60%
Therefore, the percentage of the cookies were gingerbread is 60%.
Answer:
Step-by-step explanation:
cccccc
How would increasing the value of a variable change the value of the expressions when evaluating an algebraic expression?Give two examples in your explanation.
Increasing the value of a variable change the value of the expressions
What is Expression?An expression is combination of variables, numbers and operators.
A variable in expression is a characteristic that can be measured and that can assume different values.
When the variable value is increased then the value of expression will be also increases because with the variable the value of expression is interlinked.
2x+4 is an expression
Let x=1
then 2(1)+4=6
Value of expression is 6.
If x=2 then the value of expression is 8
Now the other expression is 5x+3
For x=1, 8 is the value of expression.
For x=2, 13 is the value of expression.
as values of x increases then value of expression will be increased.
Hence, increasing the value of a variable change the value of the expressions
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HELP
The perimeter of an equilateral triangle is 9 inches more than the perimeter of a square, and the side of the triangle is 5 inches longer than the side of the square. Find the side of the triangle. (Hint: An equilateral triangle has three sides the same length.)
The side length of the equilateral triangle is 29 inches.
What is perimeter?
The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides. Area is the portion of the plane that a closed form occupies, whereas perimeter is the space surrounding the closed figure.
Here in equilateral triangle all side of the triangle is equal . Then
Perimeter of triangle = 3× side. = 3s
Now perimeter of square = 4×side = 4a
Here perimeter of an equilateral triangle is 9 inches more than the perimeter of a square
=> Perimeter of square = perimeter of triangle + 9
=> 4a = 3s+9 ---------> 1
Now side of the triangle is 5 inches longer than the side of the square.
=> s = a+5-------> 2
=> a = s-5 --------> 3
Now put 3 into 1 then,
=> 4(s-5) = 3s+9
=> 4s-20 = 3s +9
=> 4s-3s = 20+9
=> s = 29 inches.
Hence side length of the equilateral triangle is 29 inches.
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The graph of function f is shown. An exponential function on a coordinate plane passes through (minus 1, 7), (1, 2), (10, minus 1) and also intercepts the x-axis at 3 units and the y-axis at 4 units. Function g is represented by the table. x -1 0 1 2 3 g(x) 24 4 0 Which statement correctly compares the two functions? A. They have the same x- and y-intercepts. B. They have different x- and y-intercepts but the same end behavior as x approaches ∞. C. They have the same y-intercept and the same end behavior as x approaches ∞. D. They have the same x-intercept and the same end behavior as x approaches ∞.
considering the graph of exponential function given , the statement that correctly compare the function is
B. They have different x- and y-intercepts but the same end behavior as x approaches ∞.What is x and y intercepts?X - intercept and Y - intercept are the two main intercepts.
The x-intercept of a point where the line crosses the x-axis, while the y-intercept is where the line or graph crosses the y-axis.
At x - intercepts the value of y is zero h=following the given values the x intercept for function f is 3 units and 4 units for the y intercept
For function g, following the table, the x intercept is (2, 0) and the y intercept is (0, 4)
the end behavior for function f is x → ∞, y → -∞
the end behavior for function g is x → ∞, y → -∞
hence they have different x and y intercept but same end behavior
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as x-∞, f(x) →-∞ and as x-∞, f(x) → -∞
as x-∞, f(x) → ∞ and as x-∞, f(x) → ∞
as x=-∞, f(x) → ∞ and as x-∞, f(x) → ∞
as x=-∞, f(x) - ∞ and as x - ∞, f(x) → ∞
The end behavior of the graph is given as
as x → - ∞, f(x) → -∞ and as x → ∞, f(x) → -∞
What are end behaviors?The term end behavior is used to describe the effects a function or graph has as the extremes.
The end behavior of function typically says the characteristics of the function at the ends
The end behavior of the graph of the given graph is deduced to be
as x tends to negative infinity (∞), f(x) tends to negative infinity -∞
as x tends to positive infinity ∞, f(x) tends to negative infinity -∞
x ⇒ -∞ f(x) ⇒ -∞
x ⇒ ∞ f(x) ⇒ -∞
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I need answers for all 4 questions please, I can give like 50 points for this
Answer:
Step-by-step explanation:
its a bit blured
What was the second largest year-on-year increase for
females?
Average Cost (£GBP) of Car Insurance for
Males and Females over a 5 year period
789
638
Year 1
872
635
Year 2
Males
Years 1 to 2
854
Years 2 to 3
Years 3 to 4
742
Year 3
878
801
Year 4
Females
Please select the correct answer from the options shown.
890 873
Year 5
the second largest year-on-year increase for female is from year 4 to 5, which is 72.
What is bar graph?A bar graph is a graph that shows complete data with rectangular bars and the heights of bars are proportional to the values that they represent. The bars in the graph can be shown vertically or horizontally. Bar graphs are also known as bar charts and it is a pictorial representation of grouped data.
Given that, the average cost (£GBP) of car insurance for Males and Females over a 5-year period.
From the graph
The average cost (£GBP) of car insurance for Males
year 1: 789
Year 2: 872
Year 3: 854
Year 4: 878
Year 5: 890
The average cost (£GBP) of car insurance for Females
Year 1: 638
Year 2: 635
Year 3: 742
Year 4: 801
Year 5: 873
Increase in cost insurance from year 2 to 3 is 742-635 =107
Increase in cost insurance from year 3 to 4 is 801-742 =59
Increase in cost insurance from year 4 to 5 is 873-801 =72
Therefore, the second largest year-on-year increase for female is from year 4 to 5, which is 72.
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A certain car cost c dollars in August. In September, the price was cut by 20 percent. In October, the price increased by 40 percent of the previous month’s price. The price of the car at the end of October was what percent of the price in August?
The price of car in October with respect to August is given as 112%.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
Suppose the price in August be c.
Then, in September it is given as,
⇒ c - 20% × c = 4/5c
And, in October it is given as,
⇒ 4/5c + 40% × 4/5c = 28/25c
The price in October with respect to August can be obtained in percent value as follows,
Price in October ÷ Price in August × 100
⇒ 28/25c ÷ c × 100 = 112%
Hence, the price in October is 112% of the price in August.
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Kay added the numbers 3.14, 4.2, and 1.6. She estimated the sum would be about 9, but her sum was 37.2. What could she have done wrong
Answer: 16
Step-by-step explanation:
So 0.9 + 0.8 + 0.2 is approximately 2.
Then, Add the two together ( 14 + 2 = 16
So then the answer would obviously be 16
Hope this helped ^^
a student's grade is a weighted calculation as follows: homework is worth 25%, midterm exam is worth 30%, discussion is worth 15%, and final exam is worth 30%. if sam has the following averages, compute his grade.
84%
84,7%
81%
81,7%
A student's grade is a weighted calculation. Sam's grade is 83.07%
Suppose we have variables v1, v2, v3, ..., and their weights are: w1, w2, w3, ..., then the weighted average is computed by:
weighted average = v1 x w1 + v2 x w2 + v3 x w3 + ...
The following table shows the weighs and the score
Component weigh Score
Homework 25% 84%
Midterm exam 30% 84.7%
Discussion 15% 81%
Final exam 30% 81,7%
Sam's grade = 25% x 84% + 30% x 84.7% + 15% x 81% + 30% x 81.7%
= 83.07%
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Envision stem the roots of plants are often the largest part of the plant. winter rye can grow combined root tissue well over 984,000 feet in length. write this number in expanded form.
984,000 = 900,000 + 80,000 + 4000
Expanded form of 984,000:
984,000 = (9 * 10⁵) + (8 * 10⁴) + (4 * 10³)
= (9 * 100,000) + (8 * 10,000) + (4 * 1,000)
Therefore, the answer is,
∴, 900,000 + 80,000 + 4,000
What are the coordinates of the vertex of the parabola y = x2 - 2x - 1?
Answer:
(1, -2)
Step-by-step explanation:
You want the coordinates of the vertex of the parabola defined by ...
y = x² -2x -1Vertex formWe can add and subtract the square of half the x-coefficient to put the equation in vertex form:
y = x² -2x -1
y = x² -2x +(-2/2)² -1 -(-2/2)²
y = (x² -2x +1) -1 -1
y = (x -1)² -2
Comparing this to the vertex form equation ...
y = (x -h)² +k . . . . . . parabola with vertex (h, k)
we see that the vertex is ...
(h, k) = (1, -2)
The coordinates of the vertex are (1, -2).
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What is the y'intercept of the line given by the equation y = 5x + 16? !!!!
Considering the expression of a line, the y-intercept of the line given by the equation y=5x +16 is 16.
What is a linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Slope in this caseIn this case, you know that the line is y=5x + 16
where:
the slope is 5.the ordinate to the origin is 16.Finally, the y-intercept is 16.
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3) ΔWXY is an isosceles triangle with WX = WY. If WX is 3 more than four times x, xy is 7 less than five times x, and Wy is 66 less than seven times x, find x and the measure of each side.
4) Graph ΔDEF, then classify the triangle.
(a) D(8,-6) E(-1,-3) F(-2,5)
The variable values and measures of the side lengths of the isosceles triangle and type of triangles are;
3) x = 23, WX = WY = 95, XY = 108
4) (a) Triangle ΔDEF is a scalene triangle
(b) Triangle ΔDEF is an isosceles right triangle
What is an isosceles triangle?An isosceles triangle is a triangle that has a two sides of the triangle which are congruent.
The specified parameters are;
[tex]\overline{WX} \cong \overline{WY}[/tex]
WX = 3 + 4·x
XY = 5·x - 7
WY = 7·x - 66
[tex]\overline{WX} = \overline{WY}[/tex], definition of congruency
3 + 4·x = 7·x - 66, by the substitution property
7·x - 4·x = 66 + 3 = 69
3·x = 69
x = 69 ÷ 3 = 23
x = 23
The length of each side are;
WX = 3 + 4 × 23 = 95
WX = 95
WY = WX = 95
XY = 5 ×23 - 7 = 108
4) The lengths of the sides of the triangle are;
(a) DE = √((-1 - 8)² + (-3 - (-6))²) = √(90) = 3·√(10)
EF = √((-2 - (-1))² + (5 - (-3))²) = √(65)
DF = √((-2 - 8)² + (5 - (-6))²) = √(221)
The length of the sides of the triangle ΔDEF are all different, indicating the triangle is a scalene triangle. ΔDEF
(b) (a) DE = √((5 - (-2))² + (5 - 3)²) = √(53)
EF = √((5 - (-4))² + (5 - 10)²) = √(106)
DF = √((-4 - (-2))² + (10 - 3)²) = √(53)
The length of DE is congruent to DF
[tex]\overline{DE}[/tex]² = 53
[tex]\overline{DF}[/tex]² = 53
[tex]\overline{EF}[/tex]² = 106
53 + 53 = 106
Therefore;
[tex]\overline{DE}[/tex]² + [tex]\overline{DF}[/tex]² = [tex]\overline{EF}[/tex]²
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Match the property with the statement.
Transitive property of
equality
Division property of
equality
Angle congruence postulate
Subtraction property of
equality
Symmetric property of
equality
Reflexive property of
equality
1. If 7 = x then x = 7
2. p=p
3. If a = 7, a = q. q =s and s = t, then t
= 7
4. if 3x = 9 then x = 3
5.
6. 4x + 2=6 then 4x = 4
The equality's transitive property is If a = 7, then a = q, q = s, s = t, and t = 7 .The equality reflex states that if 4x Plus 2=6, then 4x must equal 6.
what is angle ?Two straight lines or rays intersect at a common endpoint to form an angle. The vertex of an angle is the point at which all points meet. Angle is derived from the Latin word angulus, which means "corner." Two rays (half-lines) combined into an angle have a single endpoint. The latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms. Two lines converge at a common point to form an angle.
given
The equality's transitive property is If a = 7, then a = q, q = s, s = t, and t = 7 .
The equality reflex states that if 4x Plus 2=6, then 4x must equal 6.
The equality's subtraction property states that if 3x = 9 then x = 3.
The premise of angle congruence is Since x = 7 if 7 = x
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I need the slope of the line please
Find the slope of the line.
Answer:
m = -6/5
Step-by-step explanation:
(-2, 4) and (3, -2)
m = -2-4/3+2
m = -6/5
Final Answer:
-6/5In-depth explanation:
Hi! The question is asking us to find the slope of the line.
We're given two points that the line passes through:
(-2,4) and (3,-2)
We can use the slope formula to find the slope:
[tex]\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
Where:
[tex]\bf{m=slope}[/tex][tex]\bf{x_1}[/tex] is the x-coordinate of the first point[tex]\bf{x_2}[/tex] is the x-coordinate of the second point[tex]\bf{y_1}[/tex] is the y-coordinate of the first point[tex]\bf{y_2}[/tex] is the y-coordinate of the second pointPlug in the data:
[tex]\bf{m=\dfrac{-2-4}{3-(-2)}}[/tex]
[tex]\bf{m=\dfrac{-6}{3+2}}[/tex]
[tex]\bf{m=\dfrac{-6}{5}}[/tex]
[tex]\bf{m=-\dfrac{6}{5}}[/tex]
Therefore, the slope of this line is -6/5.
If f(x) = 3x+1 and f^-1 = x-1/3
Then f^-1(7)=
22
-2
2
The value of the inverse function [tex]f^{-1}(7)[/tex] is 2.
What is inverse of a function?In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Let the given function is [tex]f:X\rightarrow Y[/tex]
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
[tex]f^{-1}: Y \rightarrow X[/tex]
such that:
[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]
This means, inverse of 'f' is undo operator, that takes back the effect of 'f'
We are given that f(x) = 3x+1 and [tex]f^{-1} = x-\frac{1}{3}[/tex]
Then We can find it by plugging 7 in for x in the [tex]f^{-1}(x)[/tex].
So, [tex]f^{-1}(7)[/tex] = 7-1/3
[tex]f^{-1}(7)[/tex] = 6/3
[tex]f^{-1}(7)[/tex] = 2
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Write an equation of the form y = mx for the line shown below.
(2,6)
(1,3)
Answer:
y = 3x
Step-by-step explanation:
Slope = change in y / change in x
x, y
Given points: (2,6) and (1,3)
2 - 1 = 1
6 - 3 = 3
3/1 = 3
y = mx
y = 3x
Which of these is a factor in this expression?
524 −3+8 (y³ + 7)
O A. -3+8 (y + 7)
OB. 52-3
O c. (y³ + 7)
O D. 8 (y³ +7)
Option c) The factor in the expression is (y³ + 7).
What is a Factor ?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product since the product is divisible by them.
An integer m that can be multiplied by another integer to create the number n is referred to as a divisor of an integer n, also known as a factor of n. One may also state that n is a multiple of m in this situation.
A factor is a number that is multiplied by another number to get the desired result. The answer to a multiplication puzzle is a product. Imagine multiplying the components in a multiplication problem to get the answer. For instance, the factors 2 and 4 add up to 8: Just two things or a great many factors can affect a number.
The function is
−3+8 (y³ + 7)
The factor that is in the option is (y³ + 7) . (option c)
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Evaluate 4/2 for w = 3
Answer:
is 42 3 fraction
Step-by-step explanation:
Evaluate 4/2 for w = 3
-6x^3+7x^2+3 entre 2x-3
Help!
The solution to the polynomial division is; -3x² - x - ³/₂ + (- ³/₂)/(2x - 3)
How to carry out polynomial long division?We want to use polynomial long division to divide -6x³ + 7x² + 3 by 2x - 3.
A long division polynomial is defined as an algorithm that is used to divide a polynomial by another polynomial of the same or a lower degree.
Thus, we have;
-3x² - x - ³/₂
2x - 3| -6x³ + 7x² + 3
- -6x³ + 9x²
-2x² + 3
- -2x² + 3x
-3x + 3
-3x + ⁹/₂
- ³/₂
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Identify a, b and c from the quadratic trinomial x^2-5x+6
By comparing the given equations we get the values a= 1 b = -5 and
c = 6
What is Quadratic equation ?
Quadratic equation can be defined as the equation in which it is in the form of ax^2+bx+c = 0
where c is constant.
a is the coefficient of x^2
b is the coefficient of x .
Given ,
Quadratic equation is x^2 - 5x + 6
So, the quadratic equation is always be in the form of ax^2+bx+c
and from above we can see that it is in the given form .
So,
By comparing both equations x^2 - 5x + 6 and ax^2+bx+c
So,
we get,
a = 1
b = -(5)
b = -5
c = 6
So, By comparing the given equations we get the values a= 1 b = -5 and
c = 6
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Emily is single and has earned both qualified and nonqualified dividends this year. Her taxable income is $125,000. Using this
information and the tables provided, determine how much tax Emily will pay on each type of dividend.
Type the correct answer in each box. Use numerals instead of words.
Single Taxpayers: Income Brackets
Tax Rate
10%
12%
22%
24%
32%
35%
37%
Income Bracket
O to 9.525
9.526 to 38,700
38,701 to 82.500
82.501 to 157.500
157,501 to 200,000
200,001 to 500,000
>500,000
Single Taxpayers: Qualified Dividends
and Long-Term Capital Gains
Tax Rate
Income Bracket
0%
15%
20%
The tax rate on Emily's nonqualified dividends is
The tax rate on Emily's qualified dividends is
0 to 35,600
38,601 to 425,800
> 425,800
96. Her taxes on $500 in ordinary dividends will equal
96. Her taxes on $2,000 in qualified dividends will equal
The amount of tax paid is found applying the proportions, and the correct proportion is obtained from the table in the problem.
Her taxable income is given as follows:
$125,000.
Hence the tax proportions are given as follows:
Non-qualified: 24%, which is the rate from an income of $82,501 and $157,500.Qualified: 15%, which is the rate from an income between $38,601 and $425,800.Meaning that the taxes paid are given as follows:
$500 non-qualified: 0.24 x 500 = $120.$2000 qualified: 0.15 x 2000 = $300.More can be learned about proportions at https://brainly.com/question/24372153
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What is the dollar amount of the gentry’s annual transportation and taxes combined?
Proportionately, the dollar amount of the Gentrys' annual transportation and taxes combined is $11,004.70.
What is proportion?Proportion refers to the relative value of a number compared to another amount.
Proportions are ratios equated to one another.
Multiplying the proportional percentage of the combined transportation and taxes to the total budget of the Gentrys gives the dollar amount.
Yearly income for the Gentrys = $29,742.42
Percentage of income that is taxes = 28%
Percentage of income that is transportation = 9%
Combined percentage of taxes and transportation = 37% (28 + 9)
Combined transportation and taxes in dollars = $11,004.70 ($29,742.42 x 37%)
Thus, based on their proportional percentages, the Gentrys' combined annual transportation and taxes are $11,004.70.
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7) Jacob lives in an apartment. He has to tie an 185-meter long rope at the distance of 90 meter from the building to its roof. What is the height of the building?
8) There is a cycle ramp at the park. The ramp is mostly used by skateboarders. The incline of the ramp is 320. The height of the ramp is 10m. How long is the ramp?
HELP PLEASE :?
Using Pythagoras theorem, the height of the building is 161.6m and the length of the ramp is 319.2m
What is Pythagoras TheoremAccording to Pythagoras' Theorem, the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the two legs. It can be mathematically stated as a²+b² =c², where a and b represent the lengths of the triangle's two legs and c represents the length of the hypotenuse.
7)
Using Pythagoras's theorem, we can find the height of the ramp.
185² = 90² + b²
b² = 185² - 90²
b² = 26125
b = √26125
b = 161.6m
8)
Using Pythagoras's theorem,
x² = y² + z²
320² = 10² + z²
z² = 320² - 10²
z² = 102300
z = 319.8m
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A boat rental service charges a 20 transportation fee and 15 dollars each hour to rebt a bout. Suppose you and your best friend plan to rent a boat for 6 hours. How much money will it cost to rent the boat?
Answer:
$110
Step-by-step explanation:
$20 + ($15/hr)(6 hr) = $110
Implement pseudocode for calculating a running average of numbers. While the user continues to input numbers (e.g. in a loop), keep the running average. When the user stops, emit the average of the numbers input.
The running average is calculated by dividing the sum of all the input numbers by the number of inputs. Here is the Pseudocode:
Initialize variables: sum = 0, count = 0Start a loop that continues until the user stops inputting numbersWithin the loop, prompt the user to enter a numberAdd the number to the sum and increment the count by 1Calculate the running average by dividing the sum by the countContinue the loop until the user stops inputting numbersWhen the loop ends, emit the final average by dividing the sum by the countThe pseudocode above outlines the steps for calculating a running average of numbers input by the user. The running average is calculated by dividing the sum of all the input numbers by the number of inputs. The loop continues until the user stops inputting numbers, at which point the final average is emitted by dividing the sum by the count. This allows the user to input any number of numbers and continuously see the running average as they go.
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a simple random sample of size n is obtained from a population whose size is and whose population proportion with a specified characteristic is describe the sampling distribution of . round the standard deviation of the sampling distribution to three decimal places.
The sampling distribution of is a binomial distribution with parameters n and p, where n is the sample size and p is the population proportion of the specified characteristic.
The mean of the sampling distribution is np and the standard deviation is [tex]$\sqrt{np(1-p)}$[/tex].
Sampling Distribution of a Simple Random SampleRound the standard deviation to three decimal places, it is [tex]$\sqrt{np(1-p)}$ = $\sqrt{n \cdot p \cdot (1-p)} \approx \sqrt{n \cdot p \cdot 0.99}$[/tex].
The sampling distribution of is a binomial distribution with parameters n and p, where n is the sample size and p is the population proportion of the specified characteristic. The mean of the sampling distribution is np and the standard deviation is [tex]$\sqrt{np(1-p)}$[/tex]. This means that for a given sample size n and population proportion p, the standard deviation of the sampling distribution can be calculated by taking the square root of the product of n, p, and (1-p).
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The table shows the number of boxes needed to hold different numbers of baseballs. How many boxes are needed for 222 baseballs? Number of Baseballs Number of Boxes 492 82 486 81 480 80 474 79 468 78
Answer: this is very easy
Step-by-step explanation:
Find the surface of the cylinder. USE 3.14 for pie
Pls look at the photo and help me out :( number 6! (5mm and 2mm) pls show step by step because I have to show my work! Will be marking brainelst and giving a lot of points.
The surface area of the cylinder is 87.92 mm²
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
We need to find the surface area of cylinder.
The cylinder has radius of 2mm
Height of the cylinder is 5 mm
The surface area of cylinder=2πrh+2πr²
=2πr(r+h)
=2×3.14×2(2+5)
=12.56(7)
=87.92 mm²
Hence, the surface area of the cylinder is 87.92 mm²
To learn more on Three dimensional figure click:
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Please help with this send a screenshot with the answers
From the given figure the angles in the form as Same side interior angles, vertically opposite angles and etc.
What are parallel lines ?
Parallel lines can be defined as the lines which are equi distant from each other and they never intersect.
Given in the figure,
parallel lines and we have to find the how the angles are related to each other.
In the given figure 1 ,
The angles are Same side Interior Angles .
In the given figure 2 ,
The angles are Vertically opposite Angles .
In the given figure 3 ,
The angles are Alternate Exterior Angles .
In the given figure 4 ,
The angles are Alternate Interior Angles .
In the given figure 5 ,
The angles are Alternate Exterior Angles .
In the given figure 6 ,
The angles are Corresponding Angles .
In the given figure 8 ,
The angles are Vertically opposite Angles .
In the given figure 9,
The angles are Alternate Interior Angles .
Hence, From the given figure the angles in the form as Above.
To learn more about Parallel lines from the given link.
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