Question

Each of the exterior angles of a regular polygon is 100 degree less than the interior angle. Calculate the size of the exterior angle

Answer 1

Step-by-step explanation:

Given:-

Each of the exterior angles of a regular polygon is 100 degree less than the interior angle.

To find:-

Calculate the size of the exterior angle ?

Solution:-

Method-1:-

Let the interior angle of a regular polygon be X°

Then, Exterior angle of the regular polygon

= 100° less than the interior angle

= X° -100°

We know that

The sum of exterior and interior angles of a regular polygon = 180°

=> X°-100°+X° = 180°

=> 2X° -100° = 180°

=> 2X° = 180°+100°

=> 2X° = 280°

=> X° = 280°/2

=> X° = 140°

The interior angle = 140°

Exterior angle = 140°-100°=40°

Method-2:-

The exterior angle of a regular polygon of n sides

= 360°/n

The interior angle of a regular polygon of n sides =(n-2)×180°/n

Given that

Exterior angle of the regular polygon

= 100° less than the interior angle

=> [(n-2)×180°/n]-(360°/n) = 100°

=> [(180n-360°)/n]-(360°/n)=100°

=> (180n -360°-360°)/n = 100

=> (180n-720°)/n = 100

=> 180n -720° = 100n

=> 180n -100n = 720°

=> 80n = 720°

=> n = 720°/80

=> n = 9

Number of sides in the polygon = 9

It's a Nonagon

Each exterior angle = 360°/n

=> 360°/9

=> 40°

Answer:-

Each exterior angle of the given regular polygon is 40°

Used formulae:-

• The exterior angle of a regular polygon of n sides = 360°/n

• The interior angle of a regular polygon of n sides =(n-2)×180°/n

• The sum of exterior and interior angles of a regular polygon = 180°