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

May 5, 2018

Exterior Angle A = 80°

Explanation:

As per the question,

PQ = PR and Exterior $\angle$P = 140°

$\therefore$ $\Delta$PQR is an isosceles triangle. And hence $\angle$QPR = $\angle$QRP.

Now, Exterior $\angle$P + $\angle$QPR = 180

$\therefore$ $\angle$QPR = 180 - 140 = 40°

And as $\angle$QPR = $\angle$ QRP

$\therefore$ $\angle$QRP = 40°

Now,

$\angle$QPR + $\angle$QRP + $\angle$PQR = 180

$\angle$PQR = 180 - 40 - 40 = 100°

Now,

$\angle$A + $\angle$PQR = 180

$\angle$A = 180 - 100

$\therefore$A = 80°