Geometry math question

Question

Find the measure of the remote exterior angle. X= 6n-20  Y= 5n+11  Z= 171-n

A) 15

B)86

C) 70

D) 156

Answer 1

Then Z = X+Y   because the theorem says the exterior is supplementary to the sum of the interiors

 

 171 - n = 11n - 9   after combining X+Y

 

  171+9 = 11n + n  <---- adds n+9 to both sides

 

 180 = 12n

 

n=15

 

So the exterior is 171 - n = 171-15 = 156 which is option D

 

As a check, the interiors are X=6(15)- 20 = 90-20 = 70 and Y = 5n+11  = 5(15)+11 = 75+11 = 86

                         The total is X+y = 70+86 = 156 = Z