Question

one interior angle of a polygon is equal to 800 and each of the other interior angles are 128 degrees. Find the number of sides of the polygon.​

Answer 1

6

Explanation:

Given information:

Interior angle of a polygon cannot be more that 180°.

One interior angle =
`80^(\circ)`

Other interior angles are =
`128^(\circ)`

Let n be the number of sides of the polygon.​

Sum of interior angles is

`Sum=80+128(n-1)`

`Sum=80+128n-128`

Combine like terms.

`Sum=128n-48` .... (1)

If a polygon have n sides then the sum of interior angles is

`Sum=(n-2)180`

`Sum=180n-360` .... (2)

Equating (1) and (2) we get

`180n-360=128n-48`

Isolate variable terms.

`180n-128n=360-48`

`52n=312`

Divide both sides by 52.

`n=(312)/(52)`

`n=6`

Therefore the number of sides of the polygon is 6.