REGULAR POLYGONS 1A

An interior angle of a regular polygon is 70⁰ 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+70⁰ …………………(2)

Substitute (2) in (1) above.

e+70⁰   + e=180⁰

e+ e+70⁰   =180⁰

2e+ 70⁰   =180⁰

2e=180⁰ - 70⁰   

2e=110⁰

2e=110⁰          dividing by 2 both sides.

2      2

e = 55⁰

But from equation (2)

But i = e+70⁰

        = 55⁰+70⁰

        = 125⁰      

Hence interior angle = 125⁰      

TRY THIS………………………   

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