Which of the following angles is an exterior angle of a regular polygon?
Answer Details
An exterior angle of a polygon is an angle formed by extending one of the sides of the polygon. For a regular polygon, all the exterior angles have the same measure, which can be found by dividing the total sum of the exterior angles (which is always 360 degrees) by the number of sides. In this case, we have a list of angles and we need to determine which one is an exterior angle of a regular polygon. We can start by dividing 360 degrees by each of the answer choices and see if any of the results match the definition of an exterior angle. - 360/95 = 3.789, which is not a whole number and therefore cannot be an exterior angle of a regular polygon. - 360/85 = 4.235, which is not a whole number and therefore cannot be an exterior angle of a regular polygon. - 360/78 = 4.615, which is not a whole number and therefore cannot be an exterior angle of a regular polygon. - 360/75 = 4.8, which is a whole number and therefore could be an exterior angle of a regular polygon. We can confirm this by checking if the sum of this angle and any of the interior angles of a regular polygon add up to 180 degrees. For example, a regular pentagon has interior angles of 108 degrees, and 75 + 108 = 183, which is not 180 degrees. Therefore, 75 degrees is not an exterior angle of a regular pentagon. - 360/72 = 5, which is a whole number and therefore could be an exterior angle of a regular polygon. Again, we can confirm this by checking if the sum of this angle and any of the interior angles of a regular polygon add up to 180 degrees. For example, a regular pentagon has interior angles of 108 degrees, and 72 + 108 = 180 degrees. Therefore, 72 degrees is an exterior angle of a regular pentagon. Therefore, the answer is: 72o.