The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find:
(i) measure of each interior angle,
(ii) measure of each exterior angle and
(iii) number of sides in the polygon

Question

The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find:
(i) measure of each interior angle,
(ii) measure of each exterior angle and
(iii) number of sides in the polygon

KnowledgeBoat · Accepted Answer

(i) It is given that each interior angle of a regular polygon is five times the measure of its exterior angle. Let the exterior angles of the polygon be a. Then, the interior angle = 5 x a = 5a We know that the sum of the interior angle and the exterior angle is 180°. ⇒ a \+ 5a = 180° ⇒ 6a = 180° ⇒ a = ⇒ a = 30° So, the exterior angle is 30°. The interior angle = 5a = 5 x 30° = 150° Hence, the interior angle of the polygon is 150°. (ii) Exterior angle = a = 30° Hence, the exterior angle of the polygon is 30°. (iii) According to the properties of polygons, each interior angle of a regular polygon with n sides is . ⇒ = 150° ⇒ (2n \- 4) x 90° = 150°n ⇒ 180°n \- 360° = 150°n ⇒ 180°n \- 150°n = 360° ⇒ 30°n = 360° ⇒ n = ⇒ n = 12 Hence, the number of sides of the polygon is 12.

Mathematics

The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find:
(i) measure of each interior angle,
(ii) measure of each exterior angle and
(iii) number of sides in the polygon

Geometrical Shapes

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Mathematics

The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find:(i) measure of each interior angle,(ii) measure of each exterior angle and(iii) number of sides in the polygon

Geometrical Shapes

Related Questions

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The ratio between the exterior angle and the interior angle of a regualr polygon is 1 : 4. Find the number of sides in the polygon.

The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find:
(i) measure of each interior angle,
(ii) measure of each exterior angle and
(iii) number of sides in the polygon

The ratio between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find.
(i) each exterior angle of the polygon,
(ii) number of sides in the polygon.