JAMB 2012 Mathematics · Question 6

The angles of a polygon are given by x, 2x, 3x, 4x and 5x respectively. Find the value of x.

Options

A.24o
B.30o
C.33o
D.36o

Answer: D. 36o

Explanation written with AI and checked against the answer key

Analyze the question: The polygon has 5 angles: x, 2x, 3x, 4x and 5x. We need x. Concept: The sum of interior angles of an n-sided polygon is (n − 2) × 180°. Solution: Number of sides, n = 5 (a pentagon). Sum of interior angles = (5 − 2) × 180° = 3 × 180° = 540° Add the given angles: x + 2x + 3x + 4x + 5x = 15x So: 15x = 540° x = 540° ÷ 15 = 36° Check: The angles are 36°, 72°, 108°, 144°, 180°. Their sum is 540°, which matches. (One angle comes to 180°, which is a quirk of the question, but the intended method is the angle sum, and it gives option D.) Answer: x = 36°, which is option D. Tip: When a polygon's angles are given in terms of x, count the sides first, use (n − 2) × 180°, then add up the coefficients of x and divide. Memorize: triangle 180°, quadrilateral 360°, pentagon 540°, hexagon 720°.

AI can make mistakes. Report anything that looks wrong.