Question

your friends says that an exterior angle can never be complementary to any of the interior angles in a triangle?

Answer 1

Answer:

Two angles are complementary if their addition is equal to 90°.

As you may know, the exterior angle is equal to the addition of both opposite interior angles, so suppose that you have a triangle with two angles of 30° and one of 120° (because the addition of the 3 interior angles must be equal to 180°)

In this case, the exterior angle that is opposite of both interior angles of 30°, is equal to their sum, so this angle has 30° + 30° = 60°

Now, this angle of 60° would be complementary with bot 30° interior angles.

So given the right triangle, an exterior angle can be complementary to some interior angles.

Answer 2

Exterior angles are complementary to the opposite interior angle