WAEC 2022 Mathematics · Question 42

An exterior angle of a regular polygon is 22.5°. Find the number of sides.

Options

A.13
B.14
C.15
D.16

Answer: D. 16

Explanation written with AI and checked against the answer key

Analyze the question We're given one exterior angle of a regular polygon (22.5°) and asked for the number of sides. Concept The exterior angles of any polygon add up to 360°. In a regular polygon all exterior angles are equal, so: Number of sides, n = 360° ÷ (one exterior angle) Solution n = 360 ÷ 22.5 To remove the decimal, multiply the top and bottom by 2: n = 720 ÷ 45 = 16 Check: 16 × 22.5 = 360° ✓ The polygon has 16 sides. Tip: For regular polygons, "exterior angle" questions are always solved with n = 360 ÷ exterior angle. If given an interior angle instead, first find the exterior angle with 180° − interior angle. Also, you can quickly check that interior + exterior = 180° (here the interior angle is 157.5°).

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