Table of Contents

- 1 How do you find the measure of a central angle of a regular polygon with 10 sides?
- 2 How do you find the measure of the central angle of a regular polygon?
- 3 What is the measure of a 10 sided regular polygon?
- 4 How many sides does a regular polygon have if its central angle is 45?
- 5 What’s the angle measure of a square?
- 6 What is the sum of a 5 sided polygon?

## How do you find the measure of a central angle of a regular polygon with 10 sides?

To find the measure of the central angle of a regular decagon, make a circle in the middle… A circle is 360 degrees around… Divide that by ten angles… So, the measure of the central angle of a regular decagon is 36 degrees.

## How do you find the measure of the central angle of a regular polygon?

All central angles would add up to 360 degrees (a full circle), so the measure of the central angle is 360 divided by the number of sides. Hence, central angle = 360 / N degrees, where N is the number of sides.

**What is the measure of each angle in a 10 sided polygon?**

The sum of the measures of the interior angles of a decagon (10 sided polygon) is 1,440. We found this by using the formula (n-2)(180). Thus, to find the measure of each interior angle we simply divide the sum by the number of total sides in the polygon. 1,440/10 = 144.

### What is the measure of a 10 sided regular polygon?

1440°

In geometry, a decagon (from the Greek δέκα déka and γωνία gonía, “ten angles”) is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°.

### How many sides does a regular polygon have if its central angle is 45?

8

As each exterior angle is 45o , number of angles or sides of the polygon is 360o45o=8 .

**What is the measure of each angle in a regular polygon with 9 sides?**

140°

The General Rule

Shape | Sides | Each Angle |
---|---|---|

Octagon | 8 | 135° |

Nonagon | 9 | 140° |

… | … | … |

Any Polygon | n | (n−2) × 180° / n |

## What’s the angle measure of a square?

90°

All four angles of a square are equal (each being 360°/4 = 90°, a right angle). All four sides of a square are equal. The diagonals of a square are equal.

## What is the sum of a 5 sided polygon?

540°

In geometry, a pentagon (from the Greek πέντε pente meaning five and γωνία gonia meaning angle) is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°….Regular pentagons.

Regular pentagon | |
---|---|

Type | Regular polygon |

Edges and vertices | 5 |

Schläfli symbol | {5} |

Coxeter diagram |

**What shape has 45 degree angles?**

regular octagon

So, the measure of the central angle of a regular octagon is 45 degrees.