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Problem 853

AMC 12 late, AIME early

Geometry Difficulty 4.5 Find the answer HMMT February

A regular decagon $A_{0} A_{1} A_{2} \cdots A_{9}$ is given in the plane. Compute $\angle A_{0} A_{3} A_{7}$ in degrees.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Put the decagon in a circle. Each side subtends an arc of $360^{\circ} / 10=36^{\circ}$ . The inscribed angle $\angle A_{0} A_{3} A_{7}$ contains 3 segments, namely $A_{7} A_{8}, A_{8} A_{9}, A_{9} A_{0}$ , so the angle is $108^{\circ} / 2=54^{\circ}$ .

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.