The exterior angles of a pentagon are in the ratio 1 : 2 : 3 : 4 : 5. Find its interior angles.
Geometrical Shapes
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The exterior angles of a pentagon are in the ratio 1 : 2 : 3 : 4 : 5. Find its interior angles.

KnowledgeBoat · Accepted Answer

It is given that the exterior angles of a pentagon are in the ratio 1 : 2 : 3 : 4 : 5. Let the exterior angles be a, 2a, 3a, 4a and 5a. According to the properties of a polygon, the sum of the exterior angles is 360°. ⇒ a \+ 2a \+ 3a \+ 4a \+ 5a = 360° ⇒ 15a = 360° ⇒ a = ⇒ a = 24° The exterior angles are, = 24°, 2 x 24°, 3 x 24°, 4 x 24° and 5 x 24° = 24°, 48°, 72°, 96° and 120° The interior angles are calculated by subtracting the exterior angles from 180°: 180° \- 24° = 156° 180° \- 48° = 132° 180° \- 72° = 108° 180° \- 96° = 84° 180° \- 120° = 60° Hence, the interior angles are 60°, 84°, 108°, 132° and 156°.

Mathematics

The exterior angles of a pentagon are in the ratio 1 : 2 : 3 : 4 : 5. Find its interior angles.

Geometrical Shapes

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