# How many sides a regular polygon whose interior angle measures twice its exterior?

## How many sides a regular polygon whose interior angle measures twice its exterior?

Since each interior angle is twice its adjacent exterior angle, therefore, substitute i=2e. We know that the measure of exterior angle is e=( where n is the number of sides. Hence, the number of sides is 6.

For what type of polygon is the sum of the interior angles twice the sum of the exterior angles?

a regular polygon
The sum of interior angles of a regular polygon is twice the sum of its exterior angles.

### What is the measure of an interior angle of a polygon with an exterior angle of 24?

Each exterior angle measures 36024=15 . The interior angle measures 180−15=165 . The sum of the 24 interior angles is then 24⋅165=3960 .

What does an interior angle plus an exterior angle of a polygon always add to?

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 is pentagon sides?

Answer- The Pentagon has 5 (five) sides. A pentagon is a five-sided polygon also known as 5-gon in geometry. 540° is the sum of internal angles of a simple pentagon.

How many sides does a regular polygon have if each of its interior angle is 140 degree?

n = 9 sides.

## What is the sum of an exterior angle and interior angle of a polygon at a vertex?

180°
The sum of the internal angle and the external angle on the same vertex is 180°.

What is the sum of interior and exterior of a regular polygon?

Interior and exterior angle formulas: The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180. If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°.

### What polygon has an exterior angle of 15?

The polygon has 24 sides.

How do you find the exterior angles of a polygon?

The sum of exterior angles of a polygon is 360°. The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides.

#### What is sum of exterior angle of pentagon?

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 do you find exterior angles of a polygon?

To find the value of a given exterior angle of a regular polygon, simply divide 360 by the number of sides or angles that the polygon has. For example, an eight-sided regular polygon, an octagon, has exterior angles that are 45 degrees each, because 360/8 = 45.

## What is the measure of each exterior angle of a regular polygon?

Since the sum of exterior angles of any polygon is always equal to 360°, we can divide by the number of sides of the regular polygon to get the measure of the individual angles. For example, for a pentagon, we have to divide 360° by 5: 360°÷5 = 72° Each exterior angle in a regular pentagon measures 72°.

What is the measure of the exterior angle of an octagon?

The sum of measure of all the interior angles of polygon is = (n -2) 180°. Since octagon has eight sides therefore sum of interior angels is = 6×180 =1080° and since it is a regular octagon therefore each angle measure is 1080÷8 = 135°. Therefore exterior angle is supplement of 180° i.e 180–135 =45°.

### What is a regular polygon?

A regular polygon is a geometric figure that has all its sides with the same length and all its interior angles with the same measure. This means that all of its exterior angles also have the same measure.

How to find the measure of a single interior angle?

In order to find the measure of a single interior angle of a regular polygon (a polygon with sides of equal length and angles of equal measure) with n sides, we calculate the sum interior anglesor $$(\\red n-2) \\cdot 180$$ and then divide that sum by the number of sides or $$\\red n$$.