Convex Pentagon

Question

1. Suppose you have a convex pentagon with interior angles that measure 110 degrees, 80 degrees, 72 degrees 62 degrees for four of its vertices. Which of the following statements are true for the convex polygon? Select all that apply.

1. The measure of the fifth angle is 216.

2. The pentagon is concave

3. The sum of the exterior angles of the polygon is greater than 360 degrees.

4. The sun of the exterior angles is 360 degrees.

5. The supplementary angle to angle C has the measure of 125 degrees.

Answer 1

The sum of the measures of the interior angles of a convex polygon is (n-2)*180, where n is the number of sides, so the sum of the measures of the interior angles for a convex pentagon is 3 * 180 = 540.

Thus the measure of the 5th angle = 540 - 110 - 80 - 72 - 62 = 216.

The sum of the measures of the exterior angles of a convex polygon is 360 degrees.

1 and 4.