Question

Find the measures of an exterior angle and an interior angle given the number of sides of each regular polygon. Round to the nearest tenth, if necessary. 24 b 15, 345 24, 156 7.5, 172.5 15, 165​

Answer 1

The measure of exterior and interior angles in a regular polygon can be found by dividing 360 by the number of sides and subtracting from 180, respectively.

Step-by-step explanation:

The measure of an exterior angle of a regular polygon can be found by dividing 360 by the number of sides of the polygon. To find the measure of an interior angle, subtract the exterior angle from 180. Let's take the examples given:

1. For a polygon with 24 sides, the exterior angle measure would be 360/24 = 15 degrees. The interior angle measure would be 180 - 15 = 165 degrees.
2. For a polygon with 15 sides, the exterior angle measure would be 360/15 = 24 degrees. The interior angle measure would be 180 - 24 = 156 degrees.
3. For a polygon with 7.5 sides, the concept of a fraction of a side is not applicable for regular polygons. Therefore, we cannot find the measure of the angles.

Answer 2

Answer: Find the measures of an exterior angle and an interior angle given the number of sides of each regular polygon. Round to the nearest tenth, if necessary. 24 b 15, 345 24, 156 7.5, 172.5 15, 165​

Step-by-step explanation: sum, S, of the measure of the interior angles of a polygon with n sides is: ... The sum of the interior angles of a 24 -gon is 3960. ... angles of a polygon is (n−2)⋅180 , where n is the number of sides. ... Each exterior angle measures 36024=15 . ... The sum of the 24 interior angles is then 24⋅165=3960 .