Oues- The ratio between an exterior angle and the interior angle of a regular polygon is 1:5. Find(i) the measure of each exterior angle (ii) the measure of each interior angle(iii) the number of sides in the polygon. it is of Math's ..

Oues- The ratio between an exterior angle and the interior angle of a

1.	Oues- The ratio between an exterior angle and the interior angle of a regular polygon is 1:5. Find(i) the measure of each exterior angle (ii) the measure of each interior angle(iii) the number of sides in the polygon. it is of Math's ..
Answer» TION: Given that ratio between an EXTERIOR angle and the interior angle = 1:5.We know that measure of an interior angle = (n - 2)(180/n) and the measure of an exterior angle = (360/n).1/5 = (360/n) / (n - 2)(180/n)1/5 = (360/n) / n/(n - 2) * 1801/5 = (360/n) / n(180n - 360)1/5 = (360)/(180(n - 2))1/5 = 2/(n - 2)1(n - 2) = 5 * 2n - 2 = 10n = 12.Therefore the number of sides in the POLYGON = 12.(1) Therefore the measure of each exterior angle = 360/(n) = 360/12 = 30.(2) Therefore the measure of each interior angle = 180 - 30 = 150.Hope this helps!