Question

In triangle ABC, the measure of the exterior angle at point B is 100°. If angle A 17°, what is angle C?

Answer 1

`color(blue)("Angle " C=83^@)`

Explanation:

The exterior angle and the adjacent interior are supplementary, so they add up to `180^@`

So for angle at B:

`100^@+theta=180^@=>theta=80^@`

All the interior angle add to `180^@`

`:.`

`17^@+80^@+theta=180^@`

`theta=180^@-(17^@+80^@)=83^@`

Angle `C=83^@`