Question

What is the sum of the measures of the exterior angles of a convex decagon?

Answer 1

For ANY polygon you have Interior and Exterior angles. There is a formula that you can use to get the sum of the interior angles, and eventually to solve this question

The sum of the interior angles in a polygon with n sides is 180º(n – 2). {Obtained from internet. Also in any textbook on Polygons}

**We know the decagon to have 10 sides
With the formula we get the sum of the internal angles as
180(10-2) = 180(8) = 1440 (degrees)
Divide by 10 to get 144 (degrees) as the measure of the interior angle at ONE vertex
*We did so because we want to compare the Interiror and Exterior Angles for a single vertex
The interior and exterior add to give 180 (degrees) So to get the exterior:
Exterior = 180 -144 = 36
So the answer to the question would be:
36 *10 = 360 (degrees)