Recall that the sum of the interior angle measures of an n-sided convex polygon is (n-2)180.
157.5
Practice makes perfect
Let's begin with recalling the Polygon Interior Angles Sum Theorem.
The sum of the interior angle measures
of an n-sided convex polygon is(n-2)180.In our exercise, we are asked to find the measure of each interior angle of a regular polygon with 16 sides. First, let's find the sum of the interior angle measures of this polygon by substituting 16 for n in the above formula.
Since the given polygon is regular, all interior angles are congruent. This means that to find the measure of each of the interior angles, we need to divide the sum of all interior angles, 2520, by the number of sides, which is 16.
2520/16=157.5
Each interior angle of this polygon measures 157.5.
