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boyakko [2]
3 years ago
5

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

Mathematics
1 answer:
pishuonlain [190]3 years ago
3 0

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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<em><u>HAVE</u></em><em><u> </u></em><em><u>A</u></em><em><u> </u></em><em><u>GREAT</u></em><em><u> </u></em><em><u>DAY</u></em><em><u> </u></em>

<em><u>#Liliflim</u></em>

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