POLYGONS 1

An interior angle of a regular polygon is 74⁰ 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+74⁰ …………………(2)

Substitute (2) in (1) above.

e+74⁰   + e=180⁰

e+ e+74⁰   =180⁰

2e+ 74⁰   =180⁰

2e=180⁰ - 74⁰   

2e=106⁰

2e=106⁰          dividing by 2 both sides.

2      2

e = 53⁰

But i  + e=180⁰…………………(1)

i  + 53⁰=180⁰.

i  =180⁰ - 53⁰

i = 127⁰

Hence i = 127⁰ 

TRY THIS………………………   

An interior angle of a regular polygon is 78⁰ greater than an exterior angle. Find the interior angle.