Question

A triangle has the measures of two of its interior angles 48° and 65°, the third interior angle is unknown. What is the value of the exterior angle corresponding to the interior angle whose value is unknown?

a) 123°
b) 131°
c) 113°
d) 128°
e) 118°

Answer 1

c) 113°

Explanation:

Exterior angle is equal to the sum or the "remote" interior angles, that is the two angles that are not just next to the exterior angle. See image.

So the answer, quickly:

exterior angle

= 65° + 48°

= 113°

This is why:

(skip if you don't care)

The three angles in a triangle add up to 180° But also, a linear pair of angles also add up to 180°

So

x + 65° + 48° = 180°

x + y = 180°

y = 65° + 48°

See image.