The polygon is not about the political parties only. There may be scenarios once you have more than one shape with the same variety of sides.

You are watching: What is the measure of each exterior angle

How to identify them then? ANGLES!

The simplest instance is that both rectangle and a parallelogram have actually 4 sides each, through opposite sides room parallel and also equal in length. The difference lies in angles, wherein a rectangle has 90-degree angles on its all 4 sides while a parallelogram has opposite angles of equal measure.

How to uncover the angle of a polygon?Interior angle of a polygon.Exterior angle of a polygon.How to calculate the size of each interior and exterior edge of a regular polygon.

## How to uncover the angles of a Polygon?

We understand that a polygon is a two-dimensional multi-sided figure consisted of of straight-line segments. The sum of angles of a polygon is the total measure of all interior angles of a polygon.

Since every the angles inside the polygons room the same. Therefore, the formula for finding the angle of a continuous polygon is provided by;

Sum of inner angles = 180° * (n – 2)

Where n = the variety of sides of a polygon.

Examples

Angles of a Triangle:

a triangle has actually 3 sides, therefore,

n = 3

Substitute n = 3 into the formula of detect the angles of a polygon.

Sum of internal angles = 180° * (n – 2)

= 180° * (3 – 2)

= 180° * 1

= 180°

A square is a 4-sided polygon, therefore,

n = 4.

By substitution,

sum of angles = 180° * (n – 2)

= 180° * (4 – 2)

= 180° * 2

= 360°

Angles the a Pentagon

A pentagon is a 5 – sided polygon.

n = 5

Substitute.

Sum of inner angles = 180° * (n – 2)

=180° * (5 – 2)

= 180° * 3

= 540°

Angles of one octagon.

An Octagon is an 8 – sided polygon

n = 8

By substitution,

Sum of internal angles = 180° * (n – 2)

= 180° * (8 – 2)

= 180° * 6

= 1080°

Angles that a Hectagon:

a Hectagon is a 100-sided polygon.

n = 100.

Substitute.

Sum of internal angles = 180° * (n – 2)

= 180° * (100 – 2)

= 180° * 98

= 17640°

### Interior angle of polygons

The inner angle is an angle developed inside a polygon, and it is in between two political parties of a polygon.

The variety of sides in a polygon is equal to the variety of angles formed in a details polygon. The size of each inner angle of a polygon is offered by;

Measure that each interior angle = 180° * (n – 2)/n

where n = variety of sides.

Examples

Size the the internal angle that a decagon.

A decagon is a 10 -sided polygon.

n = 10

Measure that each internal angle = 180° * (n – 2)/n

Substitution.

= 180° * (10 – 2)/10

= 180° * 8/10

= 18° * 8

= 144°

Interior angle of a Hexagon.

A hexagon has 6 sides. Therefore, n = 6

Substitute.

Measure the each internal angle =180° * (n – 2)/n

= 180° * (6 – 2)/6

= 180° * 4/6

= 60° * 2

= 120°

Interior edge of a rectangle

A rectangle is an instance of a square (4 sides)

n = 4

Measure of each internal angle =180° * (n – 2)/n

=180° * (4 – 2)/4

=180° * 1/2

=90°

Interior angle of a pentagon.

A pentagon is created of 5 sides.

n = 5

The measure of each inner angle =180° * (5 – 2)/5

=180° * 3/5

= 108°

### Exterior edge of polygons

The exterior edge is the edge formed outside a polygon between one next and an extensive side. The measure of each exterior angle of a regular polygon is given by;

The measure up of each exterior angle =360°/n, where n = number of sides of a polygon.

One crucial property around a constant polygon’s exterior angles is that the amount of the measures of the exterior angles of a polygon is constantly 360°.

Examples

Exterior angle of a triangle:

For a triangle, n = 3

Substitute.

Measure of every exterior angle = 360°/n

= 360°/3

= 120°

Exterior angle of a Pentagon:

n = 5

Measure of every exterior angle = 360°/n

= 360°/5

= 72°

NOTE: The inner angle and also exterior edge formulas only job-related for constant polygons. Irregular polygon have various interior and exterior measures of angles.

Let’s watch at an ext example problems about interior and exterior angle of polygons.

Example 1

The internal angles of an rarely often, rarely 6-sided polygon are; 80°, 130°, 102°, 36°, x°, and also 146°.

Calculate the dimension of edge x in the polygon.

Solution

For a polygon with 6 sides, n = 6

the sum of internal angles =180° * (n – 2)

= 180° * (6 – 2)

= 180° * 4

= 720°

Therefore, 80° + 130° + 102° +36°+ x° + 146° = 720°

Simplify.

494° + x = 720°

Subtract 494° indigenous both sides.

494° – 494° + x = 720° – 494°

x = 226°

Example 2

Find the exterior angle of a continuous polygon with 11 sides.

Solution

n =11

The measure of every exterior angle= 360°/n

= 360°/11

≈ 32.73°

Example 3:

The exterior angle of a polygon are; 7x°, 5x°, x°, 4x° and x°. Recognize the worth of x.

Solution

Sum that exterior =360°

7x° + 5x° + x° + 4x° + x° =360°

Simplify.

18x = 360°

Divide both political parties by 18.

x = 360°/18

x = 20°

Therefore, the value of x is 20°.

Example 4

What is the name of a polygon whose interior angles space each 140°?

Solution

Size that each internal angle = 180° * (n – 2)/n

Therefore, 140° = 180° * (n – 2)/n

Multiply both political parties by n

140°n =180° (n – 2)

140°n = 180°n – 360°

Subtract both sides by 180°n.

140°n – 180°n = 180°n – 180°n – 360°

-40°n = -360°

Divide both sides by -40°

n = -360°/-40°

Therefore, the number of sides is 9 (nonagon).

### Practice Questions

The very first four inner angles the a pentagon room all, and also the fifth angle is 140°. Discover the measure of the 4 angles.Find the measure up of a polygon’s eight angle if the first seven angles are 132° each.Calculate the angles of a polygon which are given as; (x – 70) °, x°, (x – 5) °, (3x – 44) ° and (x + 15) °.The proportion of a hexagon’s angle is; 1: 2: 3: 4: 6: 8. Calculation the measure of the angles.What is the surname of a polygon having each inner angle as 135°?