Question

The Measure of the interior angles is a convex octagon increases by 8 degrees for each angles. What is the Largest angle?

Answer 1

The sum of the interior angles of an octagon is 1080 degrees (2n-4)×180, so each angle of a regular octagon measures 135 degrees (1080/8).

Since the measure of the interior angles of this convex octagon increases by 8 degrees for each angle, the smallest angle measures 135 degrees and each successive angle is 8 degrees larger. Therefore, the largest angle is:

135 + (8×7) = 199 degrees

So the largest angle measures 199 degrees.