WAEC 2020 Mathematics · Question 19
Each interior angle of a regular polygon is 168. Find the number of sides of the polygon
Options
- A.30
- B.36
- C.24
- D.18
Answer: A. 30
Explanation written with AI and checked against the answer key
Analyze the question: We are given one interior angle of a regular polygon (168°) and must find the number of sides, n. Concept: The interior and exterior angles at a vertex lie on a straight line, so they add up to 180°. The exterior angles of any polygon add up to 360°. In a regular polygon all exterior angles are equal, so: Number of sides = 360° ÷ (exterior angle) Solution: Exterior angle = 180° − 168° = 12° n = 360° ÷ 12° = 30 Check using the interior angle formula: Interior angle = (n − 2) × 180° / n (n − 2) × 180 / n = 168 180n − 360 = 168n 12n = 360 n = 30 ✓ Answer: A. 30 Tip: When you are given an interior angle of a regular polygon, go straight to the exterior angle (180° − interior) and divide 360° by it. It is faster and less error-prone than rearranging the interior angle formula.AI can make mistakes. Report anything that looks wrong.
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