Question

Find the measure of each interior angle of a regular polygon having (i) 10 sides (ii) 15 sides

Answer 1

We know that each interior angle of a regular polygon of n sides = $\frac{2n-4}{n}$ right angle (i) Polygon having 10 sides, each interior angle = $\frac{2\times 10-4}{10}$ = $\frac{16}{10}$ right angles = $\frac{16}{10}{90}^{\circ }={144}^{\circ }$ (ii) Polygon having 15 sides, each interior angle = $\frac{2\times 15-4}{15}$ right angles = $\frac{26}{15}\times {90}^{\circ }={156}^{\circ }$