JAMB Mathematics 2021 Paper

Concept:For a regular polygon, each interior angle is found by dividing the total sum of its interior angles by the number of sides.Explanation:Let $n$ be the number of sides of the polygon.The sum of interior angles of an $n$-sided polygon is $(n - 2) \times 180^\circ$.Thus, each interior angle is:$$\frac{(n - 2) \times 180^\circ}{n}$$Given that each interior angle is $140^\circ$, we write:$$140 = \frac{(n - 2) \times 180}{n}$$Multiply both sides by $n$:$$140n = 180n - 360$$Collect like terms:$$180n - 140n = 360$$$$40n = 360$$Divide both sides by $40$:$$n = \frac{360}{40} = 9$$Answer:The polygon has $9$ sides.Correct option: A.