Question

Find the measure of each exterior angle of a regular

(i) Pentagon

(ii) Hexagon

(iii) Heptagon

(iv) Decagon

(v) Polygon of 15 sides.

Answer 1

(i) In a regular pentagon, all sides are same size and measure of all interior angles are

Same.

The sum of interior angles of pentagon is

(n-2) × 180^o where n is the number of sides of polygon.

(5-2) × 180^o = 540^o here n=5 because penta means 5

Each interior angle= 540/5 = 108^o

As we know that the sum of interior and exterior angle is 180⁰

Exterior angle + interior angle = 180⁰

Exterior angle + 108^o= 180⁰

Exterior angle = 180⁰– 108^o= 72⁰

(ii) In a regular hexagon, all sides are same size and measure of all interior angles are

Same.

The sum of interior angles of pentagon is

(n-2) × 180^o where n is the number of sides of polygon.

(6-2) × 180^o = 720^o here n=6 because hexa means 6

Each interior angle= 720/6 = 120^o

As we know that the sum of interior and exterior angle is 180⁰

Exterior angle + interior angle = 180⁰

Exterior angle + 120^o= 180⁰

Exterior angle = 180⁰– 120^o= 60⁰

(iii) In a regular heptagon, all sides are same size and measure of all interior angles are

Same.

The sum of interior angles of heptagon is

(n-2) × 180^o where n is the number of sides of polygon.

(7-2) × 180^o = 900^o here n=7 because hepta means 7

Each interior angle= 900/7 = 128.57^o

As we know that the sum of interior and exterior angle is 180⁰

Exterior angle + interior angle = 180⁰

Exterior angle + 128.57^o= 180⁰

Exterior angle = 180⁰– 128.57^o= 51.43⁰

(iv) In a regular decagon, all sides are same size and measure of all interior angles are

Same.

The sum of interior angles of decagon is

(n-2) × 180^o where n is the number of sides of polygon.

(10-2) × 180^o =1440^o here n=10 because deca means 10

Each interior angle= 1440/10 = 144^o

As we know that the sum of interior and exterior angle is 180⁰

Exterior angle + interior angle = 180⁰

Exterior angle + 144^o= 180⁰

Exterior angle = 180⁰– 144^o= 36⁰

(v) In a regular polygon, all sides are same size and measure of all interior angles are

Same.

The sum of interior angles of polygon of 15 sides is

(n-2) × 180^o where n is the number of sides of polygon.

(15-2) × 180^o =1440 ^o here n=15

Each interior angle= 2340/15 = 156^o

As we know that the sum of interior and exterior angle is 180⁰

Exterior angle + interior angle = 180⁰

Exterior angle + 156^o= 180⁰

Exterior angle = 180⁰– 156^o= 24⁰