# Why are the exterior angles of a polygon 360?

**360**. Geometric proof: When all of the

**angles**of a convex

**polygon**converge, or pushed together, they form one

**angle**called a perigon

**angle**, which measures

**360**degrees. If the sides of the convex

**polygon**are increased or decreased, the sum of all of the

**exterior angle**is still

**360**degrees.

Similarly, you may ask, do all polygons exterior angles add up to 360?

The **sum** of **exterior angles in** a **polygon is** always equal to **360** degrees. Therefore, for **all** equiangular **polygons**, the measure of one **exterior angle is** equal to **360** divided by the number of sides **in** the **polygon**.

Additionally, do all polygons add up to 360? Remember that **all** of the sides of regular **polygon** and **all** of its angles are equal. Memorise the rule that an interior angle and its corresponding angle **add up** to 180°, and that **all** of the exterior angles of a **polygon add up to 360**°.

Herein, what is the exterior angle sum of a polygon?

The **sum** of the measures of the **exterior angles** of a **polygon**, one at each vertex, is 360°.

What is the formula for exterior angles?

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.