In the figure, P is hte centre of an excircle of ▲ ABC. If ∠ABC=40° and ∠BAC=80°, find the angle measure of triangle APC.
60°
Given, ∠BAC=80°
Therefore, ∠EAC=100° [Linear pair(∠BAC+∠EAC=180°)]
∠PAC=12×100=50°
Also, ∠APC=90°−12∠ABC [∠ABC = 40°, given]
= 90° - 20° = 70°
∠PCA=180°−(50°+70°)=60°