Question

an exterior angle of a triangle is 105 and its two interior opposite angles are equal then what is measure of these two equal angles?

Answer 1

In a triangle, the sum of two interior opposite angles is equal to the exterior angle.

=> For ∆ABC, exterior angle C = angle A + angle B


So in the question, we are given that the interior opposite angles are equal and the exterior angle to them is of 105°

Let the interior opposite angles be x

=> x + x = 105

=> 2x = 105

=> x = 105/2

=> x = 52.5°

So, the measure of these two angles is 52.5°

Answer :- 52.5°




Additional details :-

The third angle would form linear pair with the exterior, so third angle = 180 - 105 = 75°

Answer 2

let angle x = angle y (givin)

105° + angle x = 180° ( linear pair)
angle x = 180°-105° = 75°

angle x = angle y (givin)
75° = angle y


angle x = 75°
angle y = 75°

I hope it will help you..
Thank you :-)