Question

The interior angles of a polygon is 100. The other interior angles are 110. How many sides has the polygon?

Answer 1

Answer:

There is a formula for the total interior angles of a polygon:

180(sides−2)= total interior angles

One of the angles is 100 and all the others are 110.

We can rewrite the equation.

Assume there is x number of sides.

There are x−1 number of angles, 110 degrees

180(x−2)=100+110(x−1)

180x−360=100+110x−110

70x−360=100−110

70x−360=−10

70x=3507x=35

x=5

There are 5 sides to the polygon.

We can check our answer:

180(sides−2)= total interior angles

sides=180(5−2)=100+4(110)

180∗3=100+440

540=540