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The measure of each interior angle of a regular polygon is 157.5 degrees . How many sides doesthe polygon have?

The measure of each interior angle of a regular polygon is 157.5 degrees . How many-example-1
User Jaredhoyt
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1 Answer

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given the interior angle of the regular polygon as 157.5 degrees

to solve this,

we subtract the interior angle angle from 180, divide the result into 360 to get the number of sides

so,

lets use this formular

180(n-2) = 157.5n

opening the bracket

180n - 360 = 157.5n

collecting like times

180n - 157.5n = 360

22.5n = 360

divide both sides by 22.5

22.5n/22.5 = 360/22.5

n = 16

therefore, the polygon has 16 sides

User Scorpiozj
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