How to find the measure of an interior angle of a regular polygon

How do you find the interior angle of a regular polygon?

(n-2)x 180 degrees : The formula for finding the sum of all angles in a polygon ( REGULAR ). Here “n” represents the number of sides of the polygon .

How do you find the measure of one interior angle?

The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides. The sum of exterior angles of a polygon is 360°.

What is the interior angle of a polygon?

The interior angles of a polygon are those angles at each vertex that are on the inside of the polygon . There is one per vertex. So for a polygon with N sides, there are N vertices and N interior angles . Notice that for any given number of sides, all the interior angles are the same.

How do you find the interior angle of a regular pentagon?

All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the interior angles , we know that the sum of all the angles is 540 degrees (from above) And there are five angles So, the measure of the interior angle of a regular pentagon is 108 degrees.

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 .

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How do you figure out how many sides a polygon has?

Finding the Number of Sides of a Polygon 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.

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 one interior angle of a regular hexagon?

And there are six angles So, the measure of the interior angle of a regular hexagon is 120 degrees .

What is the interior angle of a 7 sided polygon?

A regular heptagon, in which all sides and all angles are equal, has internal angles of 5π/ 7 radians (128​47 degrees). Its Schläfli symbol is { 7 }.

How many sides does a polygon have if the sum of its interior angles is 720?

The General Rule

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Shape Sides Sum of Interior Angles
Triangle 3 180 °
Quadrilateral 4 360°
Pentagon 5 540°
Hexagon 6 720°

What is interior angle with example?

Mathwords: Interior Angle . An angle on the interior of a plane figure. Examples : The angles labeled 1, 2, 3, 4, and 5 in the pentagon below are all interior angles . Angles 3, 4, 5, and 6 in the second example below are all interior angles as well (parallel lines cut by a transversal).

What is the interior angle of a pentagon?

108°

What is the measure of each interior angle of a regular 16 Gon?

Each angle of a regular hexadecagon is 157.5 degrees, and the total angle measure of any hexadecagon is 2520 degrees.

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