2012-04-27 09:00:13

If each angle of a regular hexagon measures x degrees and each angle of a regular pentagon measures y degrees, what is (x - y)²?

The correct answer is 144

Explanation: A regular hexagon is a hexagon of six sides that are equal in measure and six angles equal in measure. A hexagon contains 720°, so each angle of a regular hexagon is just 720/6, or 120°. Thus, x = 120. A regular pentagon is a pentagon of five sides that are equal in measure and five angles equal in measure. A pentagon contains 540°, so each angle of a regular hexagon is just 540/4, or 108°. Thus, y = 1o8.

To find (x - y)², plug 120 in for x and 108 in for y: (120 - 108)² = 12². 12² is 144, so the correct answer is 144.