The interior angle of a polygon is 100 . The other interior angle are all equal to 110. how many sides has the polygon?

Question

asked Oct 1, 2022 30.6k views

1 Answer

Niels Robben · Answer 1 · 2022-10-04T21:33:05+0000

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

Therefore it is true:

The polygon has 5 sides

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