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Use the diagram to find the measure of exterior angle BCD.

Triangle A B C has angles labeled as follows: A, (101x + 2) degrees; B, 34x degrees; C, unlabeled. Point C lies on Ray A D. The outside angle B C D is labeled (138x - 1) degrees. left parenthesis 138 x minus 1 right parenthesis degrees(138x − 1)°

34 x degrees34x° left parenthesis 101 x plus 2 right parenthesis degrees(101x + 2)° DCAB

 

The measure of exterior angle BCD is

 

cassie19  Nov 29, 2017
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 #1
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(101x + 2) + 34x + C = 180, solve for C
C =178 - 135x
(178-135x) + (138x - 1) = 180, solve for x
x = 1, so:
Angle BCD =(138x1 -1) =137 Degrees.

Guest Nov 29, 2017
edited by Guest  Nov 29, 2017
 #2
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By the exterior angle theorem.....angle BCD  = angle A + angle B  ....so....

 

138x - 1   =  101x + 2  + 34x       simplify

 

138x - 1  =  135x + 2        subtract 135x from both sides, add 1 to both sides

 

3x  =  3    divide both sides by 3

 

x  = 1

 

So   BCD  =  138(1) - 1   =   137°

 

 

cool cool cool

CPhill  Nov 29, 2017

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