How many sides has a regular polygon whose exterior angle is 1/5 of the interior angle?

12 sides
Given, there is a polygon whose exterior and interior angles are in the ratio 1:5. Let, there be n sides of that polygon. As, the sum of interior angles of any polygon is calculated by (n−2)×180∘ and sum of the exterior angle is equal to 360∘ . Therefore, there are 12 sides in the given polygon.

What is the sum of all exterior angles of a pentagon?

360°
This means: Sum of exterior angles = 180n – 180(n-2) = 180n – 180n + 360. Hence, the sum of exterior angles of a pentagon equals 360°.

How many sides does a polygon have if the measure of each exterior angle is 18 What is the sum of the measures of the interior angles?

The polygon has 20 sides.

What is the exterior angle of a regular polygon?

The sum of the exterior angles of a polygon is 360°. The formula for calculating the size of an exterior angle in a regular polygon is: 360. If you know the exterior angle you can find the interior angle using the formula: interior angle + exterior angle = 180°

What polygon has exterior angles of 5?

regular pentagon
A regular pentagon is a polygon with 5 sides of equal measure.

How do you calculate interior angles of a polygon?

Note down the number of sides “n.”

To find the interior angles of a polygon,use the formula,Sum of interior angles = (n-2)×180°

To find each interior angle of a polygon,then use the general formula,Each angle of regular polygon =[(n-2)×180°]/n

Substitute the given side value in the formula to get the solution.

How do you find the sum of the interior angles of a polygon?

The sum of a pentagon’s interior angles is taken by multiplying 180 by 3, which is equivalent to 540. In general, the formula for obtaining the sum of all interior angles of any polygon is (n-2) multiplied by 180 degrees, where “n” indicates the number of sides.

How to calculate the sum of the exterior angles of a polygon?

How to Calculate the Sum of the Exterior Angles of a Polygon Regular Polygons. The angles of a regular polygon are equivalent, and their sides are as well. Irregular Polygons. The sum of the exterior angles of an irregular polygon also equals 360 degrees, even though the angles are not equivalent. Checking the Values of Exterior Angles. Finding the Sides of a Regular Polygon from an Exterior Angle.

What are the interior angles of a regular polygon?

In a regular polygon all angles are congruent So each exterior angle is 360/12, or 30 degrees. Each interior angle is the supplement of the exterior (interior + exterior =180). So each interior angle is 180–30, or 150 degrees.