The interior angles of a convex polygon add up to 2340°. How many diagonals does this polygon have?

Question

Accepted Answer

90. The angle sum of an n-sided polygon is (n − 2) × 180°, so (n − 2) × 180 = 2340 gives n − 2 = 13 and n = 15. The number of diagonals is n(n − 3)/2 = 15 × 12/2 = 90.

The interior angles of a convex polygon add up to 2340°. How many diagonals does this polygon have?

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Geometry practice