(i) If all the angles of a hexagon are equal, find the measure of each angle.
(ii) If all the angles of a 14-sided figure are equal, find the measure of each angle.

Question

(i) If all the angles of a hexagon are equal, find the measure of each angle. (ii) If all the angles of a 14-sided figure are equal, find the measure of each angle.

KnowledgeBoat · Accepted Answer

(i) According to the properties of a polygon, if a polygon has n sides, then the sum of its interior angles is (2n \- 4) x 90°. A hexagon has 6 sides. So, the sum of its interior angles is: (2 x 6 \- 4) x 90° = (12 \- 4) x 90° = 8 x 90° = 720° Since it is given that all angles are equal, let each angle be a. ⇒ 6a = 720° ⇒ a = ⇒ a = 120° Hence, the measure of each angle is 120°. (ii) According to the properties of a polygon, if a polygon has n sides, then the sum of its interior angles is (2n \- 4) x 90°. A polygon with 14 sides is given. So, the sum of its interior angles is: (2 x 14 \- 4) x 90° = (28 \- 4) x 90° = 24 x 90° = 2160° Since it is given that all angles are equal, let each angle be a. 14a = 2160° ⇒ a = ⇒ a = ⇒ a = Hence, the measure of each angle is .

Mathematics

(i) If all the angles of a hexagon are equal, find the measure of each angle.
(ii) If all the angles of a 14-sided figure are equal, find the measure of each angle.

Geometrical Shapes

Related Questions

Find the number of sides in a polygon if the sum of its interior angles is 16 right angles.

Is it possible to have a polygon whose sum of interior angles is:
(i) 870°
(ii) 2340°
(iii) 7 right angles ?

Find the sum of exterior angles obtained on producing the sides of a polygon, in order, with 7 sides.

The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are (6x - 1)°, (10x + 2)°, (8x+ 2)°, (9x - 3)°, (5x + 4)° and (12x + 6)°, find each exterior angle.

Mathematics

(i) If all the angles of a hexagon are equal, find the measure of each angle.(ii) If all the angles of a 14-sided figure are equal, find the measure of each angle.

Geometrical Shapes

Related Questions

Find the number of sides in a polygon if the sum of its interior angles is 16 right angles.

Is it possible to have a polygon whose sum of interior angles is:(i) 870°(ii) 2340°(iii) 7 right angles ?

Find the sum of exterior angles obtained on producing the sides of a polygon, in order, with 7 sides.

The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are (6x - 1)°, (10x + 2)°, (8x+ 2)°, (9x - 3)°, (5x + 4)° and (12x + 6)°, find each exterior angle.

(i) If all the angles of a hexagon are equal, find the measure of each angle.
(ii) If all the angles of a 14-sided figure are equal, find the measure of each angle.

Is it possible to have a polygon whose sum of interior angles is:
(i) 870°
(ii) 2340°
(iii) 7 right angles ?