Question

6) A sketch os a backyard gazebo shows a floor that is a regular pentagon. All floorboards need to be cut at the same angle so the pieces fit together. At what angles does each floorboard need to be cut?

Answer 1

In a regular pentagon, all the interior angles are equal. To determine the angle at which each floorboard needs to be cut, we can divide the interior angle sum of a pentagon by the number of sides (floorboards) to get the measure of each angle.

Let's calculate it step by step:

1. Interior Angle Sum of a Pentagon:

The formula to find the interior angle sum of a polygon is (n-2) * 180 degrees, where n is the number of sides. For a pentagon, n = 5, so the interior angle sum is (5-2) * 180 = 540 degrees.

2. Measure of each Angle:

To find the measure of each angle, we divide the interior angle sum by the number of sides (floorboards) in the pentagon. In this case, each floorboard represents a side, so we divide 540 degrees by 5:

Measure of each angle = 540 degrees / 5 = 108 degrees.

Therefore, each floorboard needs to be cut at an angle of 108 degrees to fit together in a regular pentagon gazebo.