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?

Given :

An exterior angle of the triangle $=$ 105 degrees.

Interior opposite angles are equal.

To do :

We have to find the measure of angles.

Solution :

Let the measure of each interior opposite angle be x degrees.

We know that,

The exterior angle of a triangle is equal to the sum of its opposite interior angles.

Therefore,

$x+x=105$ 

$2x=105$

$x=\frac{105}{2}$

 

$x=52.5$

The measure of each of the opposite interior angles is 52.5 degrees.