POLYGONS 3

An interior angle of a regular polygon is 78⁰ 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+78⁰ …………………(2)

Substitute (2) in (1) above.

e+78⁰   + e=180⁰

e+ e+78⁰   =180⁰

2e+ 78⁰   =180⁰

2e=180⁰ - 78⁰   

2e=102⁰

2e=102⁰          dividing by 2 both sides.

2      2

e = 51⁰

But i  + e=180⁰…………………(1)

i  + 51⁰=180⁰.

i  =180⁰ - 51⁰

i = 129⁰

Hence i = 129⁰ 

TRY THIS………………………   

An interior angle of a regular polygon is 82⁰ greater than an exterior angle. Find the interior angle.