# A regular polygon has 10 sides. Find the measure of each interior angle. Please show all work. Mahalo!?

The sum of the interior angles of a polygon with n sides is 2n - 4 right-angles.
With n = 10, this gives:
90(2*10 - 4)
= 1440deg.

That makes each angle 1440/10 = 144deg.
The sum of the measures of the angles of a convex polygon of n sides is
(n-2)180°.
Therefore, the sum of the measures of the angles in your 10-sided polygon is
(10-2)180°=1440°.
As the polygon is regular, measures of all interior angles are equal, and the measure of each interior angle is
1440°/10 = 144°
the sum of the angles inside of a polygon should add to 360 degrees.
10 angles present
360/10= 36 degrees each.
It`s always simpler to use the exterior angle theorem. The sum of the exterior angles of any polygon is always 360 deg. Since this has 10 sides, and it`s regular, then each exterior angle will be 360/10 = 36 deg, so each interior angle will be 180 - 36 = 144 deg. Hope this helps, Twiggy.

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