WAEC Mathematics 2012 Paper

Concept:The angles marked outside the polygon are its exterior angles, and their sum is always $360^\circ$.Each interior angle is supplementary to the adjacent exterior angle.Explanation:The exterior angles are $3x$, $2x$, $2x$, $x$, and $4x$.So, $3x + 2x + 2x + x + 4x = 360^\circ$.This simplifies to $12x = 360^\circ$.Hence, $x = \frac{360^\circ}{12} = 30^\circ$.The largest interior angle corresponds to the smallest exterior angle, which is $x = 30^\circ$.Therefore, largest interior angle $= 180^\circ - 30^\circ = 150^\circ$.Answer:Largest interior angle $= 150^\circ$.Correct option: D. $150^\circ$.