GEOMETRY B2

 

An interior angle of a regular polygon is 62⁰ 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+28⁰ …………………(2)

 

Substitute (2) in (1) above.

 

e+62⁰   + e=180⁰

 

e+ e+62⁰   =180⁰

 

2e+ 62⁰   =180⁰

 

2e=180⁰ - 62⁰   

 

2e=118⁰

 

2e=118⁰          dividing by 2 both sides.

2      2

 

e = 59⁰

 

But i  + e=180⁰…………………(1)

 

i  + 59⁰=180⁰.

 

i  =180⁰ - 59⁰

 

i = 121⁰

 

Hence i = 121⁰ 

  

TRY THIS………………………   

 

The interior angle of a regular polygon is 74⁰ greater than an exterior angle. Find the interior angle.