ACT Math · Angles and polygons

A triangle's exterior angle is formed by extending one side. The two remote interior angles measure 50° and 65°. What is the measure of…

A triangle's exterior angle is formed by extending one side. The two remote interior angles measure 50° and 65°. What is the measure of the exterior angle?

Answer and explanation

Answer: B: 115°

The exterior angle theorem says an exterior angle of a triangle equals the sum of the two remote (non-adjacent) interior angles. So the exterior angle is 50∘+65∘=115∘50^\circ+65^\circ=115^\circ, choice B. Check: the third interior angle is 180∘−50∘−65∘=65∘180^\circ-50^\circ-65^\circ=65^\circ, and its supplement is 180∘−65∘=115∘180^\circ-65^\circ=115^\circ. Choice A (65∘65^\circ) is the adjacent interior angle, not the exterior one. Choice C (130∘130^\circ) doubles the 65∘65^\circ angle. Choice D (180∘180^\circ) is the sum of all three interior angles, not an exterior angle.

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