POLYGONS 1

An interior angle of a regular polygon is 88⁰ 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+88⁰ …………………(2)

Substitute (2) in (1) above.

e+88⁰   + e=180⁰

e+ e+88⁰   =180⁰

2e+ 88⁰   =180⁰

2e=180⁰ - 88⁰   

2e=92⁰

2e=92⁰            [dividing by 2 both sides].

2     2

e = 47⁰

From (1),

i  + e=180⁰

i  + 47⁰=180⁰

i  =180⁰ - 47⁰

i  =133⁰ answer

TRY THIS………………………   

An interior angle of a regular polygon is 44⁰ greater than an exterior angle. Find the interior angle.