SOLUTION: If the measure of each interior angle of a regular polygon is 176, find the number of sides in the polygon.

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Question 1152296: If the measure of each interior angle of a regular polygon is 176, find the number of sides in the polygon.
Found 3 solutions by Theo, MathLover1, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
each exterior angle in a regular polygon is equal to 180 minus the interior angle.
that makes the exterior angle equal to 180 - 176 = 4 degrees.
the number of sides in the regular polygon is equal to 360 divided by the number of degrees in the exterior angle.
that makes the number of side equal to 360 / 4 = 90.

the formula based on the interior angle is:
i = 180 * (n - 2) / n
i is the measure of the interior angle
n is the number of sides.
the formula becomes:
176 = 180 * (n - 2) / n
multiply both sides by n and simplify to get:
176 * n = 180 * n - 360
add 360 to both sides of this equation and subtract 176 * n from both sides of this equation to get:
360 = 180 * n - 176 * n
combine like terms to get:
360 = 4 * n
solve for n to get n = 360 / 4 = 90

your solution is that the number of side of the regular polygon is 90.






Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!


Let be the number of sides of a regular polygon whose interior angles are each °.
Then
° where is the number of sides
so:
° ....substitute interior angle °









Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

If the measure of each interior angle of a regular polygon is 176, find the number of sides in the polygon. 
Being a REGULAR polygon, ALL ∠s are congruent.

As EACH interior ∠ = 176o, each EXTERIOR ∠ = 180 - 176 = 4o

The sum of the EXTERIOR angles of ANY polygon is 360o, and so, number of sides of THIS polygon = 

That's it!! Nothing too complex! 

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