in triangle ABC, bisectors of angle A and angle C cross each other in point M. find angle ABC if it is half of AMC. (no shape given)
Answers
Answer:
[tex]\angle ABC=60[/tex]
Step-by-step explanation:
[tex][Kindly\ refer\ the\ image\ attachment.]\\We\ are\ given\ that,\\AM\ is\ the\ Angle\ Bisector\ of\ \angle BAC.\\Hence,\\\angle BAM= \angle MAC\\CM\ is\ the\ Angle\ Bisector\ of\ \angle BCA.\\Hence,\\\angle BCM= \angle MCA.\\Also,\\\angle AMC=2 \angle ABC[/tex]
[tex]Now,\\As\ we\ can\ observe\ that,\\\angle BCM + \angle MCA= \angle BCA\\\angle MCA+ \angle MCA= \angle BCA\ [\angle BCM = \angle MCA]\\Hence,\\2 \angle MCA= \angle BCA\\Or, \\\angle MCA=\frac{\angle BCA}{2} \\\\Similarly,\\\angle BAM + \angle MAC= \angle BAC\\\angle MAC + \angle MAC= \angle BAC\\2 \angle MAC = \angle BAC\\Or,\\\angle MAC=\frac{\angle BAC}{2}[/tex]
[tex]Through\ the\ Angle\ Sum\ Property\ of\ a\ Triangle,\ we\ know\ that:\\'The\ Sum\ of\ all\ interior\ angles\ of\ a\ triangle\ is\ 180.'\\Hence,\\In\ \triangle BAC,\\\angle ABC + \angle BCA + \angle CAB=180\\In\ \triangle MAC,\\\angle MAC+ \angle ACM + \angle AMC=180[/tex]
[tex]Hence,\\As\ \angle AMC= 2 \angle ABC, \angle MCA=\frac{\angle BCA}{2}, \angle MAC=\frac{\angle BAC}{2},\\2 \angle ABC+\frac{\angle BCA}{2}+\frac{\angle BAC}{2}=180\\By\ resolving\ the\ denominators,\\\frac{4 \angle ABC+\angle BCA+\angle BAC}{2}=180\\\\By\ comparing\ the\ Sum\ of\ angles\ in\ both\ the\ triangles,\\We\ find\ that\ the\ RHS\ of\ both\ the\ equations\ are\ equal\ i.e.180,\\The\ LHS\ of\ the\ equations\ are\ equal\ too.\\[/tex]
[tex]Hence,\\\angle ABC+ \angle BCA + \angle BAC=\frac{4 \angle ABC+\angle BCA+\angle BAC}{2}\\Hence,\\2(\angle ABC+ \angle BCA + \angle BAC)=4 \angle ABC+\angle BCA+\angle BAC\\Hence,\\2 \angle ABC+ 2 \angle BCA + 2 \angle BAC=4 \angle ABC+\angle BCA+\angle BAC\\Hence,\\2 \angle BCA + 2 \angle BAC-\angle BCA- \angle BAC=4 \angle ABC- 2 \angle ABC\\Hence,\\\angle BCA+\angle BAC= 2\angle ABC[/tex]
[tex]Lets\ get\ back\ to\ the\ Angle\ Sum\ of\ \triangle ABC,\\\angle ABC + \angle BAC + \angle ACB=180\\Hence,\\As\ \angle BCA + \angle BAC= 2 \angle ABC,\\\angle ABC + 2 \angle ABC=180\\Hence,\\3 \angle ABC=180\\\angle ABC=\frac{180}{3}=60[/tex]
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Answers
Answer:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
Step 1: Simplify both sides of the equation.
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Step 3: Subtract 9 from both sides.
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Answer:
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Step-by-step explanation:
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Answers
Step-by-step explanation:
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Answers
Answer:
the answer to this is 7.8
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Answers
Answer:
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Step-by-step explanation:
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Answers
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Answers:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Answers
Answer:
Si
Step-by-step explanation:
You take a taxi for a distance of 4 miles. You paid $6 for the trip Your friend uses the same taxi company to travel 10 miles , and pays 10.50. How much does the taxi company charge per mile, how much is the taxi company’s initial fare?please answer it’s almost due :(((
Answers
Answer:
$3 initial fare, 0.75 per mile
Step-by-step explanation:
let x be initial fare, y be per mile
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Frogfly2015 avatar
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Frogfly2015 avatar
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Step-by-step explanation:
trust
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Answers
Answer:
The amount Raphael spend on DVD including tax is $16.2
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
It would be in the order it is
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answer:
d)-8
Step-by-step explanation:
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Answers
Answer:
C
Step-by-step explanation:
Given
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C
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A new app charges an annual fee plus an additional fee per new game downloaded. The table shows the linear relationship between the number of new games downloaded and the total cost including the annual fee. Which statement is true?
A.
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The correct answer is below:
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Answer:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Answers
Answer:
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Step-by-step explanation:
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14.4x - 28.2 > 36.6
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Answers
Answer:
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Step-by-step explanation:
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[tex] d\sqrt{(x_2 - x_1)^{2}+ (y_2 - y_1)^{2} } [/tex]
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[tex] d = \sqrt{(x_2 - x_1)^{2}+ (y_2 - y_1)^{2} } \\ d = \sqrt{(3 - 3)^{2} + (9 - 4)^{2} } \\ d = \sqrt{(0)^{2} + (5)^{2} } \\ d = \sqrt{0 + 25} \\ d = \sqrt{25} \\ d = \sqrt{5} [/tex]
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158, 155,152,...
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Answers
Answer:
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Step-by-step explanation:
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lmk if im wrong so i can fix it
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
in think it's fence b okm
You sell bracelets for $2 each and necklaces for $3 each at a local flea market.
You collect $95, selling a total of 37 jewelry items. How many of each type of
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