Each interior angle of a regular polygon is 144°. Find the interior angle of a regular polygon which has double the number of sides as the first polygon.
Geometrical Shapes
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Question

Each interior angle of a regular polygon is 144°. Find the interior angle of a regular polygon which has double the number of sides as the first polygon.

KnowledgeBoat · Accepted Answer

It is given that each interior angle of a regular polygon is 144°. According to the properties of polygons, if a regular polygon has n sides, each of its interior angles . ⇒ = 144° ⇒ (2n \- 4) x 90° = 144°n ⇒ 180°n \- 360° = 144°n ⇒ 180°n \- 144°n = 360° ⇒ 36°n = 360° ⇒ n = ⇒ n = 10 So, the first polygon has 10 sides. The number of sides of the second polygon is double that of the first polygon: n = 2 x 10 = 20 For this second polygon, each of its interior angles is . ⇒ Angle = = = = = 162° Hence, the interior angle of the second polygon is 162°.

Mathematics

Each interior angle of a regular polygon is 144°. Find the interior angle of a regular polygon which has double the number of sides as the first polygon.

Geometrical Shapes

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