WAEC Mathematics 2023 Paper

Concept:For a regular polygon, the sum of exterior angles is always $360^\circ$, and each interior angle equals the exterior angle subtracted from $180^\circ$.Explanation:Let the number of sides be $n$.Each exterior angle of a regular polygon is:$$\text{Exterior angle} = \frac{360^\circ}{n}$$Each interior angle of a regular polygon is:$$\text{Interior angle} = \frac{(n-2) \times 180^\circ}{n}$$Given: interior angle $= 6 \times$ exterior angle.So,$$\frac{(n-2) \times 180}{n} = 6 \times \frac{360}{n}$$Multiply both sides by $n$:$$(n-2) \times 180 = 2160$$$$180n - 360 = 2160$$$$180n = 2160 + 360$$$$180n = 2520$$$$n = \frac{2520}{180} = 14$$Thus, the polygon has 14 sides.Answer:$n = 14$ sides, which is option D.