GEOMETRY J1

 

An interior angle of a regular polygon is 76⁰ greater than an exterior angle. Find the interior angle.

 

Solution

 

Let i = interior angle, e = exterior angle.

 

Now i  + e=180⁰…………………(1)

 

But i = e+76⁰ …………………(2)

 

Substitute (2) in (1) above.

 

e+76⁰   + e=180⁰

 

e+ e+76⁰   =180⁰

 

2e+ 76⁰   =180⁰

 

2e=180⁰ - 76⁰   

 

2e=104⁰

 

2e=104⁰          dividing by 2 both sides.

2     2

 

e = 52⁰

 

From (1),

 

i  + e=180⁰

 

i  + 52⁰=180⁰

 

i  =180⁰ - 52⁰

 

i  =128⁰ answer

 

Hence interior angle is 128⁰

 

TRY THIS………………………   

 

An interior angle of a regular polygon is 48⁰ greater than an exterior angle. Find the interior angle.