WAEC Mathematics 2016 Paper

Concept:In any regular polygon, each pair of interior and exterior angles lies on a straight line, so their sum is $180^\circ$.The number of sides is found by dividing $360^\circ$ by the exterior angle.Explanation:Let the exterior angle be $e$ and the interior angle be $a$.Given the ratio $\frac{e}{a} = \frac{1}{11}$, we have $a = 11e$.At each vertex, $a + e = 180^\circ$ because the angles form a straight line.Substitute $a = 11e$ into the equation: $11e + e = 180^\circ$.This simplifies to $12e = 180^\circ$.Thus, $e = \frac{180^\circ}{12} = 15^\circ$.For a regular polygon, the number of sides $n$ is given by $n = \frac{360^\circ}{e}$.So, $n = \frac{360^\circ}{15^\circ} = 24$.Answer:The polygon has 24 sides.Option B is correct.