# How Many Sides Does A Regular Polygon Have If The Measure Of One Interior Angle Is 150?

## What is the formula for interior angles?

You can use the same formula, S = (n − 2) × 180° S = ( n – 2 ) × 180 ° , to find out how many sides n a polygon has, if you know the value of S , the sum of interior angles..

## What is the formula for the sum of interior angles in a polygon?

(n-2)x 180 degrees : The formula for finding the sum of all angles in a polygon (REGULAR).

## How many sides does a polygon with an interior angle of 165 have?

24Hence, the regular polygon with interior angle each measuring 165 degrees is a 24-sided polygon.

## What regular polygon has an interior angle of 150?

regular dodecagonSo, the measure of the interior angle of a regular dodecagon is 150 degrees.

## How many sides has a regular polygon?

Names of Regular PolygonsRegular PolygonNumber of SidesInterior AnglesEquilateral triangle3 sides3 interior angles of 60°Square4 sides4 interior angles of 90°Regular pentagon5 sides5 interior angles of 108°Regular hexagon6 sides6 interior angles of 120°2 more rows

## What is a 9 sided figure called?

enneagonIn geometry, a nonagon (/ˈnɒnəɡɒn/) or enneagon (/ˈɛniəɡɒn/) is a nine-sided polygon or 9-gon. The name nonagon is a prefix hybrid formation, from Latin (nonus, “ninth” + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century.

## How many sides does a regular polygon have if the measure of an exterior angle is 24?

Since the sum of the exterior angles is always 360 degrees, if you divide 360 degrees by 24 degrees you get 15 which is the number of equal exterior angles and therefore 15 vertices and sides to the polygon.

## How many sides does a regular polygon have if the exterior angle is 45?

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

## How do you find the number of sides of a polygon with one interior angle?

Subtract the interior angle from 180. For example, if the interior angle was 165, subtracting it from 180 would yield 15. Divide 360 by the difference of the angle and 180 degrees. For the example, 360 divided by 15 equals 24, which is the number of sides of the polygon.

## What is the formula for a 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 many sides does a polygon with an interior angle of 160 have?

18 sidesAnswer and Explanation: Hence, it has 18 sides.

## What is the sum of a 10 sided shape?

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° .

## How many sides does a regular polygon have if the exterior angle is 30?

12Explanation: Sum of exterior angles of every polygon irrespective of number of its sides is 360o . As it is a regular polygon, all exterior angles are equal and are 30o . Hence number of sides of the polygon is 360o30o=12 .

## How many sides does a regular polygon have if each of its interior angle is 140 degree?

Answer and Explanation: The number of sides in a regular n-gon is n . Then the sum of all its interior angles is 180(n−2) 180 ( n − 2 ) degrees.

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

1 Answer. Binayaka C. The polygon is Hexakaidecagon having 16 sides.