Julio L. answered • 26d

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A **convex polygon** is defined as a **polygon** with all its **interior angles** less than 180°. This means that all the vertices of the **polygon** will point outwards, away from the **interior** of the shape.

The sum of the interior angles in a polygon depends on the number of sides it has. The **Polygon Sum Formula** states that for any n−gon, the interior angles add up to (n−2)×180∘.

→n=8

(8−2)6×180°=1,080°

Once you know the number of sides you substitute. N = 8

As you can see there are 8 sides to this polygon.

**IF YOU WANT TO FIND THE MEASURE FOR EACH ANGLE**

**Regular Polygon Interior Angle Formula:** For any equiangular n−gon, the measure of each angle is (n−2)×180∘n.

In the picture below, if all eight angles are congruent then each angle is

(8−2)×180°

-----------------

N

6×180°

-----------

N

1080°

---------

N

Angle = 135°

Each angle is 135°

**BUT IF YOU WANT TO KNOW THE NUMBER OF SIDES THEN**

The interior angles of a polygon add up to 3960°∘. How many sides does it have?

**Use the Polygon Sum Formula and solve for ****n****.**

(n−2) x 180°= 3960°

180°n − 360° = 3960°

180°n -360° + 360° = 3960° + 360°

180°n = 4320°

--------- --------

180° = 180°

n = 24 sides

**WHAT IS MEASURE OF EACH ANGLE?**

(n−2)×180°

-----------------

n

(24-2)x180°

------------------

24

22x180°

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24

Angle = 165°

If you want to check your math?

MULTIPLY 24 X 165° = 3960°