Unit 3 parallel and perpendicular lines Homework 2, please help quickly

Answer:

Step-by-step explanation:

Since, lines l and m are parallel and a transverse is intersecting these lines.

5). (9x + 2)° = 119° [Alternate intrior angles]

    9x = 117 ⇒ x = 13

6). (12x - 8)° + 104° = 180°

     12x = 180 - 96

     x = [tex]\frac{84}{12}[/tex] ⇒ x = 7

7). (5x + 7) = (8x - 71) [Alternate exterior angles]

    8x - 5x = 71 + 7

    3x = 78

    x = 26

8). (4x - 7) = (7x - 61) [Corresponding angles]

    7x - 4x = -7 + 61

    3x = 54

    x = 18

9). (9x + 25) = (13x - 19) [Corresponding angles]

    13x - 9x = 25 + 19

    4x = 44

    x = 11

   (13x - 19)° + (17y + 5)° = 180°[Linear pair of angles are supplementary]

    (13×11) - 19 + 17y + 5 = 180

    129 + 17y = 180

    17y = 180 - 129

     y = 3

10). (3x - 29) + (8y + 17) = 180 [linear pair of angles are supplementary]

     3x + 8y = 180 + 12

     3x + 8y = 192 -----(1)

     (8y + 17) = (6x - 7) [Alternate exterior angles]

     6x - 8y = 24

     3x - 4y = 12 -----(2)

     Equation (1) - equation (2)

     (3x + 8y) - (3x - 4y) = 192 - 12

     12y = 180

     y = 15

     From equation (1),

     3x + 8(15) = 192

     3x + 120 = 192

    x = 24

11). (3x + 49)° = (7x - 23)° [Corresponding angles]

    7x - 3x = 49 + 23

    4x = 72 ⇒ x = 18

    (11y - 1)° = (3x)° [Corresponding angles]

    11y = 3×18 + 1

     11y = 55 ⇒ y = 5  

12). (5x - 38)° = (3x - 4)° [Corresponding angles]

     5x - 3x = 38 - 4

     2x = 34

     x = 17

     (7y - 20)° + (5x - 38)° + 90° = 180°

     [Sum of interior angles of a triangle = 180°]

     7y + 5x - 58 = 90

     5x + 7y = 148

     5×17 + 7y = 148

     85 + 7y = 148

     7y = 148 - 85

     y = [tex]\frac{63}{7}=9[/tex]

Angles can be congruent based n several theorems; some of these theorems are: corresponding angles, vertical angles, alternate exterior angles and several others.

The values of x and y are:

Question 5:

Angles (9x + 2) and 119 are alternate angles.

Alternate angles are equal. So, we have:

[tex]\mathbf{9x +2 = 119}[/tex]

Subtract 2 from both sides

[tex]\mathbf{9x = 117}[/tex]

Divide both sides by 9

[tex]\mathbf{x = 13}[/tex]

Question 6:

Angles (12x - 8) and 104 are interior angles.

Interior angles add up to 180. So, we have:

[tex]\mathbf{12x -8 + 104 = 180}[/tex]

Collect like terms

[tex]\mathbf{12x = 180 - 104 + 8}[/tex]

[tex]\mathbf{12x = 84}[/tex]

Divide both sides by 12

[tex]\mathbf{x = 7}[/tex]

Question 7:

Angles (5x + 7) and (8x - 71) are alternate exterior angles.

Alternate exterior angles are equal. So, we have:

[tex]\mathbf{5x + 7 = 8x - 71}[/tex]

Collect like terms

[tex]\mathbf{8x - 5x= 71 + 7}[/tex]

[tex]\mathbf{3x= 78}[/tex]

Divide both sides by 3

[tex]\mathbf{x= 26}[/tex]

Question 8:

Angles (4x - 7) and (7x - 61) are corresponding angles.

Corresponding angles are equal. So, we have:

[tex]\mathbf{4x - 7 = 7x - 61}[/tex]

Collect like terms

[tex]\mathbf{4x - 7x = 7 - 61}[/tex]

[tex]\mathbf{- 3x = -54}[/tex]

Divide both sides by -3

[tex]\mathbf{x = 18}[/tex]

Question 9:

Angles (9x + 25) and (13x - 19) are corresponding angles.

Corresponding angles are equal. So, we have:

[tex]\mathbf{9x + 25 = 13x - 19}[/tex]

Collect like terms

[tex]\mathbf{9x -13x = -25 - 19}[/tex]

[tex]\mathbf{-4x = -44}[/tex]

Divide both sides by -4

[tex]\mathbf{x = 11}[/tex]

Angles (17y + 5) and (13x - 19) are supplementary angles.

So, we have:

[tex]\mathbf{17y + 5 = 13x - 19}[/tex]

Substitute 11 for x

[tex]\mathbf{17y + 5 = 13\times 11 - 19}[/tex]

[tex]\mathbf{17y + 5 = 124}[/tex]

Subtract 5 from both sides

[tex]\mathbf{17y = 119}[/tex]

Divide both sides by 17

[tex]\mathbf{y = 7}[/tex]

Question 10:

Angles (3x - 29) and (6x - 7)  add up to 180

So, we have:

[tex]\mathbf{3x -29 + 6x - 7 = 180}[/tex]

Collect like terms

[tex]\mathbf{3x + 6x = 180 + 7 + 29}[/tex]

[tex]\mathbf{9x = 216}[/tex]

Divide both sides by 9

[tex]\mathbf{x = 24}[/tex]

Angles (3x - 29) and (8y + 17) are supplementary angles.

So, we have:

[tex]\mathbf{3x - 29 + 8y + 17 = 180}[/tex]

Substitute 24 for x

[tex]\mathbf{3 \times 24 - 29 + 8y + 17 = 180}[/tex]

[tex]\mathbf{43 + 8y + 17 = 180}[/tex]

Collect like terms

[tex]\mathbf{8y = 180 - 43 - 17}[/tex]

[tex]\mathbf{8y = 120}[/tex]

Divide both sides by 8

[tex]\mathbf{y = 15}[/tex]

Question 11:

Angles (7x - 23) and (49 + 3x) are corresponding angles

So, we have:

[tex]\mathbf{7x - 23 = 49 + 3x}[/tex]

Collect like terms

[tex]\mathbf{7x - 3x = 49 + 23}[/tex]

[tex]\mathbf{4x = 72}[/tex]

Divide both sides by 4

[tex]\mathbf{x = 18}[/tex]

Angles 3x and (11y - 1) are corresponding angles.

So, we have:

[tex]\mathbf{3x = 11y - 1}[/tex]

Substitute 18 for x

[tex]\mathbf{3 \times 18 = 11y - 1}[/tex]

[tex]\mathbf{54 = 11y - 1}[/tex]

Collect like terms

[tex]\mathbf{11y =54+ 1}[/tex]

[tex]\mathbf{11y =55}[/tex]

Divide both sides by 11

[tex]\mathbf{y =5}[/tex]

Question 12:

Angles (5x - 38) and (3x - 4) are corresponding angles

So, we have:

[tex]\mathbf{5x - 38 = 3x - 4}[/tex]

Collect like terms

[tex]\mathbf{5x - 3x = 38 - 4}[/tex]

[tex]\mathbf{2x = 34}[/tex]

Divide both sides by 2

[tex]\mathbf{x = 17}[/tex]

Angles (7y - 20) and (5x - 38) are angles at the other legs of a right-angled triangle.

So, we have:

[tex]\mathbf{7y - 20 +5x - 38 = 90}[/tex]

Substitute 17 for x

[tex]\mathbf{7y - 20 +5 \times 17 - 38 = 90}[/tex]

[tex]\mathbf{7y+ 27 = 90}[/tex]

Collect like terms

[tex]\mathbf{7y=- 27 +90}[/tex]

[tex]\mathbf{7y=63}[/tex]

Divide both sides by 7

[tex]\mathbf{y=9}[/tex]

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