Given a triangle PQR PQ=RQ and one of the exterior angles is 140 degrees. What is the exterior angle A equal to?

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Answer 1 · 2018-05-05T06:32:35

Exterior Angle A = 80°

As per the question,

PQ = PR and Exterior #/_#P = 140°

#:.# #Delta#PQR is an isosceles triangle. And hence #/_ #QPR = #/_#QRP.

Now, Exterior #/_ #P + #/_#QPR = 180

#:.# #/_#QPR = 180 - 140 = 40°

And as #/_ #QPR = #/_# QRP

#:.# #/_#QRP = 40°

Now,

#/_ #QPR + #/_ #QRP + #/_#PQR = 180

#/_#PQR = 180 - 40 - 40 = 100°

Now,

#/_ #A + #/_#PQR = 180

#/_#A = 180 - 100

#:.#A = 80°

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