WAEC 2012 Mathematics · Question 39

The sum of the interior angles of regular polygon is 1800o. How many sides has the polygon?

Options

A.16
B.12
C.10
D.8

Answer: B. 12

Explanation written with AI and checked against the answer key

Analyze the question: We are told the sum of the interior angles of a polygon is 1800°, and we need to find the number of sides. Concept: The sum of the interior angles of a polygon with n sides is Sum = (n − 2) × 180° Solution: (n − 2) × 180 = 1800 n − 2 = 1800 ÷ 180 n − 2 = 10 n = 12 Check: (12 − 2) × 180 = 10 × 180 = 1800° ✓ Since the polygon is regular, each interior angle is 1800 ÷ 12 = 150°, which is a sensible value (it is less than 180°). Answer: The polygon has 12 sides, which is option B. Tip: When you see "sum of interior angles", immediately write (n − 2) × 180 and divide the given sum by 180 first. If the result plus 2 is a whole number, you have your n. Also remember that the sum of exterior angles is always 360°, so for a regular polygon, each exterior angle = 360 ÷ n (here 360 ÷ 12 = 30°, and 180 − 30 = 150° ✓).

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