Question

An exterior angle of a triangle is 105° and its two interior opposite angles are equal. The measure of each of these two angles is __________.

Answer 1

Let the measure of each of the two interior opposite angles be x.

Measure of exterior angle of triangle = 105°

We know that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.

$\therefore x+x=105°$

$\Rightarrow 2x=105°$

$\Rightarrow x=\frac{105°}{2}=52.5°$

An exterior angle of a triangle is 105° and its two interior opposite angles are equal. The measure of each of these two angles is ___52.5º___.