#### What is the formula to find the measure of each interior angle of a regular polygon

## How do you find the measure of each interior angle of an irregular polygon?

It’s just that the angles aren’t all congruent, so you can’t divide by n to get the individual measures . 2) You can use the (n – 2)*180 formula to find both the sum of the interior angles of an irregular polygon and the average measure of an angle in an irregular polygon (just divide the sum by n).

## What is the sum of the interior angles of a polygon?

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°.

## How do you find the measure of an angle?

The best way to measure an angle is to use a protractor. To do this, you’ll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle’s measurement to the nearest degree.

## What is the measure of an interior angle of a regular decagon?

All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the angles, we know that the sum of all the angles is 1440 degrees (from above) And there are ten angles So, the measure of the angle of a regular decagon is 144 degrees.

## What is the measure of each angle in a regular polygon with 10 sides?

A decagon is a 10 – sided polygon, with 10 interior angles , and 10 vertices which is where the sides meet. A regular decagon has 10 equal-length sides and equal- measure interior angles . Each angle measures 144° and they all add up to 1,440° . An irregular decagon has sides and angles that are not all equal or congruent.

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

The General Rule

Shape | Sides | Sum of Interior Angles |
---|---|---|

Hexagon | 6 | 720° |

Heptagon (or Septagon) | 7 | 900° |

Octagon | 8 | 1080° |

Nonagon | 9 | 1260° |

## What is the interior angle sum of a 7 sided polygon?

A heptagon has 7 sides , so we take the hexagon’s sum of interior angles and add 180 to it getting us, 720+180=900 degrees.

## What is the sum of the interior angle of a triangle?

180°

## What is the formula for regular polygon?

You also learned the formula for finding the area of any regular polygon if you know the length of one side and the apothem: A = (n × s × a)2 A = ( n × s × a ) 2 , where n is the number of sides, s is the length of one side, and a is the apothem.

## How do you find the measure of an angle in parallel lines?

Two angles are said to be complementary when the sum of the two angles is 90°. Two angles are said to be supplementary when the sum of the two angles is 180°. When a transversal intersects with two parallel lines eight angles are produced. The eight angles will together form four pairs of corresponding angles .

## How do you find the measure of an angle given two sides?

Example Step 1 The two sides we know are Adjacent (6,750) and Hypotenuse (8,100). Step 2 SOHCAHTOA tells us we must use Cosine. Step 3 Calculate Adjacent / Hypotenuse = 6,750/8,100 = 0.8333. Step 4 Find the angle from your calculator using cos^{–}^{1} of 0.8333: