# How many sides does a polygon have if the sum of its interior angle is 8640?

## How many sides does a polygon have if the sum of its interior angle is 8640?

The rule is that a polygon with n sides has a sum on interior angles given by 180∘(n−2) . n=8640∘180∘+2=48+2=50 .

### What polygon has an interior angle of 140 degrees?

regular nonagon
And there are nine angles… So, the measure of the angle of a regular nonagon is 140 degrees.

How many sides does a regular polygon have if each interior angle is 168 degrees?

30 sides
We know that if we find the size of an exterior angle for the given regular polygon whose interior angle is \[{{168}^{\circ }}\], we can find the number of sides. Where, n is the number of sides. Therefore, there are 30 sides in the given regular polygon whose interior angle is \[{{168}^{\circ }}\].

What polygon has an interior angle of 120 degrees?

Hexagon
Answer: If an interior angle of a regular polygon measures 120°, it has 6 sides (Hexagon).

## How many sides does each convex polygon have if the sum of the interior angles is 180?

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

### What is the sum of all interior angles of a 40 sided polygon have?

6840 degrees
In geometry, a tetracontagon or tessaracontagon is a forty-sided polygon or 40-gon. The sum of any tetracontagon’s interior angles is 6840 degrees.

What is the formula of interior angles?

The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.

How many sides does a polygon have with an interior angle of 135?

8
Complete step-by-step answer: we have to find the number of sides of the polygon. Let’s start with the assumption that the number of sides be n, this means that we have n sided regular polygon whose interior angle is 135∘. Therefore, we get the number of sides that the polygon has as 8.

## What angle is 168?

One interior angle in a regular triacontagon is 168 degrees, meaning that one exterior angle would be 12°.

### How many sides does a regular polygon have if the interior angle is 160?

Step-by-step explanation: If the interior angle of a regular polygon is 160 degrees, then the exterior angle is 20 degrees. The sum of all exterior angles is 360 degrees so there must be 360/20 sides = 18 sides.

What is the measure of the interior angles of a regular twelve sided polygon?

150°
Dodecagon

Regular dodecagon
Symmetry group Dihedral (D12), order 2×12
Internal angle (degrees) 150°
Dual polygon Self
Properties Convex, cyclic, equilateral, isogonal, isotoxal

What’s a 13 sided shape called?

Tridecagon
A 13-sided polygon, sometimes also called the triskaidecagon.

## How many sides does a regular polygon have if each of its interior?

The outside angle is thus 180°-150°=30°. 30° multiplied by the number of such angles will have to be 360°. Therfore the polygon will have 360 ° 30 ° = 12 sides. The figure is a regular 12 sided polygon or dodecagon. The formula for angle sum in any n-gon is Sum= (n-2)*180. In a regular n-gon, each angle will be the average, or the sum divided by n:

### How are the interior angles of a polygon measured?

The interior angles of a polygon are equal to a number of sides. Angles are generally measured using degrees or radians. So, if a polygon has 4 sides, then it has four angles as well. Also, the sum of interior angles of different polygons is different. What is Meant by Interior Angles of a Polygon?

How to find the interior angle of a hexagon?

In this problem, the interior angle is 120 degrees, so… Simplify and solve for n. Multiply both sides by n. Expand the left side. Subtract 120n from both sides. Now add 360 to both sides. Finally, divide both sides by 60. The regular polygon has 6 sides, and this is called a hexagon.

Is the sum of interior angles and exterior angles always equal to 360?

The angles are formed by one side of the polygon and extension of the other side. The sum of an adjacent interior angle and exterior angle for any polygon is equal to 180 degrees since they form a linear pair. Also, the sum of exterior angles of a polygon is always equal to 360 degrees. Exterior angle of a polygon = 360 ÷ number of sides