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

Answer:

6

Step-by-step 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.

$n=\frac{312}{52}$

$n=6$

Therefore the number of sides of the polygon is 6.