ACT Math · Angles and polygons

What is the measure of one interior angle of a regular decagon (10 sides)?

What is the measure of one interior angle of a regular decagon (10 sides)?

Answer and explanation

Answer: C: 144°

The sum of the interior angles of a decagon is (10−2)(180∘)=1440∘(10-2)(180^\circ)=1440^\circ. In a regular decagon all 1010 angles are equal, so each is 1440∘10=144∘\frac{1440^\circ}{10}=144^\circ, choice C. Check using exterior angles: each exterior angle is 360∘10=36∘\frac{360^\circ}{10}=36^\circ, and 180∘−36∘=144∘180^\circ-36^\circ=144^\circ. Choice B (140∘140^\circ) is the interior angle of a regular nonagon. Choice A (120∘120^\circ) is the interior angle of a regular hexagon. Choice D (160∘160^\circ) is the interior angle of a regular polygon with 1818 sides.

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