GEOMETRY 1C

An interior angle of a regular polygon is 72⁰ 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+72⁰ …………………(2)

Substitute (2) in (1) above.

e+72⁰   + e=180⁰

e+ e+72⁰   =180⁰

2e+ 72⁰   =180⁰

2e=180⁰ - 72⁰   

2e=108⁰

2e=108⁰          dividing by 2 both sides.

2      2

e = 54⁰

TRY THIS………………………   

An interior angle of a regular polygon is 86⁰ greater than an exterior angle. Find the interior angle.