POLYGONS 1

An interior angle of a regular polygon is 68⁰ 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+68⁰ …………………(2)

Substitute (2) in (1) above.

e+68⁰   + e=180⁰

e+ e+68⁰   =180⁰

2e+ 68⁰   =180⁰

2e=180⁰ - 68⁰   

2e=112⁰

2e=112⁰          dividing by 2 both sides.

2      2

e = 56⁰

But i  + e=180⁰…………………(1)

i  + 56⁰=180⁰.

i  =180⁰ - 56⁰

i = 124⁰

Hence i = 124⁰ 

TRY THIS………………………   

An interior angle of a regular polygon is 84⁰ greater than an exterior angle. Find the interior angle.