(a) Let the diagram below represent a section of the polygon SEE DIAGRAM ABOVE Also, let : \(i\) represent the size of an interior angle; \(e\) represent the size of an exterior angle. Then \(\frac{i}{e} = \frac{5}{2}\) \(\implies i = \frac{5}{2}e\) But \(i + e = 180^\circ\) (sum of angles on a straight line) Substitute \(\frac{5}{2}e\) for \(i\) in the equation \(\frac{5}{2}e + e = 180^\circ\) \(\frac{7}{2}e = 180^\circ\) \(e = \frac{180^\circ \times 2}{7} = \frac{360^\circ}{7}\) Number of sides of the polygon = \(\frac{360^\circ}{\text{size of one exterior angle}}\) = \(360^\circ \div \frac{360^\circ}{7}\) \(360^\circ \times \frac{7}{360^\circ} = 7 sides\). (b) In the diagram above, < PSR = 68^\circ (interior angle of a cyclic quad = opp exterior angle) < PSQ = 68^\circ - 40^\circ = 28^\circ < PRQ = 28^\circ (angles in same segment) < SRQ = 74^\circ (interior angle of a cyclic quad = opp exterior angle) hence, < PRS = 74^\circ - 28^\circ = 46^\circ