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

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°.

A heptagon has four angles each of 132° and remaining three angles are equal. Find the size of each of the three angles.

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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.

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The angles of a pentagon are x°, (x - 10)°, (x + 20)°, (2x - 44)° and (2x - 70)°. Find the value of x.

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In quadrilateral ABCD, sides AB and DC are parallel to each other. If ∠A : ∠D = 2 : 3 and ∠B : ∠C = 7 : 8; find all the angles of quadrilateral ABCD.

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Mathematics

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

Geometrical Shapes

Related Questions

A heptagon has four angles each of 132° and remaining three angles are equal. Find the size of each of the three angles.

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.

The angles of a pentagon are x°, (x - 10)°, (x + 20)°, (2x - 44)° and (2x - 70)°. Find the value of x.

In quadrilateral ABCD, sides AB and DC are parallel to each other. If ∠A : ∠D = 2 : 3 and ∠B : ∠C = 7 : 8; find all the angles of quadrilateral ABCD.