One of the exterior angles of a triangle is 100°. The interior opposite angle is 75°. Find the measure of all the angles of the triangle?

Given :

One of the exterior angles of a triangle is 100°.

The interior opposite angle is 75°.

To do:

We have to find all the angles of triangles.

Solution :

The sum of the angles in a linear pair is 180° and the sum of the angles in a triangle is 180°.

One of the exterior angles of a triangle is 100°.

This implies the adjacent interior angle is $180°-100°=80°$

Therefore,

The two angles of a triangle are 75° and 80°.

Let the third angle be x.

$75°+80°+x = 180°$

$155° + x = 180°$

$x = 180° -155°$

$x = 25°$

The measures of the angles of the given triangle are 25°, 75°, and 80°.