Question

The measure of an interior angle of a regular octagon is how many degrees greater than the measure of an interior angle of a regular hexagon?

Answer 1

15

Explanation:

The sum of the angle measures in a polygon with n sides is 180(n-2) degrees. So, the sum of the octagon's angles is 180(8-2) = 1080 degrees. The polygon is regular, so all the angles have the same measure, which means each is 1080/8 = 135. Similarly, the sum of the angles of a hexagon is 180(6-2) = 720 degrees, which means each angle in a regular hexagon has measure 720/6 = 120.

Therefore, the desired difference is 135 - 120 = 15

Answer 2

Explanation:

Sum of interior angle of any polygon = 180* (n- 2 )

Here, n= number of sides

Sum of interior angles of regular octagon = 180 * ( 8-2) = 180 * 6 = 1080°

In regular octagon, all the angles are congruent,

So, measure of an interior angle of regular octagon = 1080/8 = 135°

Sum of interior angles of regular hexagon = 180 * ( 6-2) = 180*4 = 720°

In regular hexagon, all the angles are congruent,

So, measure of an interior angle of regular hexagon = 720/6 = 120°

The measure of an interior angle of a regular octagon is greater than the measure of an interior angle of a regular hexagon by 15°