Polygon Internal Angle

Polygon Internal Angle Calculation:

•  n =

  Number of Sides

  Number of sides

•  T =

  Triangle Count

  Number of triangles within the polygon

•  A =

  Sum of Angles

  Sum of all angles in the polygon

•  a =

  One Regular Angle

  One angle in a regular polygon, where all angles are equal

• -3 -2 -1 0 1 2 3 4 5 6 7 8 9

  Decimals

  Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.

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Polygon Internal Angle Formula

A polygon is a two-dimensional shape with three or more sides. It may be regular, where each internal angle is equal, or irregular, where internal angles are not equal.

Each polygon can be broken down into triangles, the polygon with the least number of sides. The sum of internal angles in a triangle will be 180°. We can use the knowledge of how many triangles are in each polygon and many degrees are in a triangle to determine the sum of internal angles for a polygon of any number of sides, and if it is a regular polygon any single internal angle.

Formula for counting the number of triangles (t) in a polygon of n sides:

Formula for calculating the sum of internal angles:

Formula for calculating a single internal (a) angle of a regular polygon:

Polygon Internal Angle Variables

VARIABLES INTRO - WHAT DO WE NEED TO KNOW, WHAT ARE ASSUMPTIONS

Number of Sides (n)

Count of sides in a polygon. Polygons are given names based on the number of sides they have:

Polygon Name	Number of Sides
Triangle	3
Square	4
Pentagon	5
Hexagon	6
Heptagon	7
Octagon	8
Nonagon	9
Decagon	10

Triangle Count (T)

Number of triangles that a polygon can be broken down into.

Polygon Name	Number of Triangles
Triangle	1
Square	2
Pentagon	3
Hexagon	4
Heptagon	5
Octagon	6
Nonagon	7
Decagon	8

Sum of Internal Angles (A)

The sum of all interior angles in a polygon. 180° for each triangle.

Polygon Name	Sum of Internal Angles
Triangle	180
Square	360
Pentagon	540
Hexagon	720
Heptagon	900
Octagon	1080
Nonagon	1260
Decagon	1440

Single Internal Angle (a)

In a regular polygon where all angles are equal the value of a single angle.

Polygon Name	Single Internal Angle
Triangle	60
Square	90
Pentagon	108
Hexagon	120
Heptagon	128.571
Octagon	135
Nonagon	140
Decagon	144

Polygon Internal Angle Solution

What is the sum of internal angles in a hexagon?

A hexagon is a polygon having six sides, containing four triangles, and having a sum of internal angles of 720°.

Polygon Internal Angle Triangle Example

How many triangles are in a pentagon?

Thee triangles can be drawn inside a pentagon.

Polygon Internal Angle Internal Angle Example

What is a single internal angle in a regular octagon?

A single angle in a regular octagon is 135°.