WAEC Mathematics 2021 Paper

Concept:For any polygon with $n$ sides, the sum of interior angles is $(n-2) \times 180^\circ$.A right angle equals $90^\circ$, so the given sum must be converted into degrees before equating.Explanation:Let the polygon have $k$ sides.Given sum of interior angles = $(3k-10)$ right angles.Since $1$ right angle $=90^\circ$, this sum equals $(3k-10) \times 90^\circ$.Using the standard formula, the sum is also $(k-2) \times 180^\circ$.Equate the two expressions:$$(3k-10) \times 90 = (k-2) \times 180$$Divide both sides by $90$:$$3k-10 = 2(k-2)$$$$3k-10 = 2k-4$$$$k = 6$$So the polygon is a regular hexagon.For a regular polygon, each exterior angle is $\frac{360^\circ}{k}$.Thus, exterior angle $= \frac{360^\circ}{6} = 60^\circ$.Answer:The size of the exterior angle is $60^\circ$, i.e., Option A.