The polygon is not around the political parties only. There might be scenarios as soon as you have much more than one shape with the same number of sides.

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How to differentiate them then? ANGLES!

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

In this article, you will learn:

How to uncover the angle of a polygon?Interior angles of a polygon.Exterior angles of a polygon.How to calculation the size of every interior and exterior angle of a consistent polygon. 

How to discover the angles of a Polygon?

We know that a polygon is a two-dimensional multi-sided figure made up of straight-line segments. The amount of angles of a polygon is the total measure of all internal angles that a polygon.

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

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

Where n = the variety of sides that a polygon.

Examples

Angles of a Triangle:

a triangle has 3 sides, therefore,

n = 3

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

Sum of inner angles = 180° * (n – 2)

= 180° * (3 – 2)

= 180° * 1

= 180°

Angles that a Quadrilateral:

A square is a 4-sided polygon, therefore,

n = 4.

By substitution,

sum of angle = 180° * (n – 2)

= 180° * (4 – 2)

= 180° * 2

= 360°

Angles of a Pentagon

A pentagon is a 5 – face polygon.

n = 5

Substitute.

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

=180° * (5 – 2)

= 180° * 3

= 540°

Angles of one octagon.

An Octagon is one 8 – sided polygon

n = 8

By substitution,

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

= 180° * (8 – 2)

= 180° * 6

= 1080°

Angles the a Hectagon:

a Hectagon is a 100-sided polygon.

n = 100.

Substitute.

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

= 180° * (100 – 2)

= 180° * 98

= 17640°

Interior edge of polygons

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

The number of sides in a polygon is equal to the variety of angles created in a specific polygon. The size of each inner angle that a polygon is offered by;

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

where n = variety of sides.

Examples

Size of the internal angle that a decagon.

A decagon is a 10 -sided polygon.

n = 10

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

Substitution.

= 180° * (10 – 2)/10

= 180° * 8/10

= 18° * 8

= 144°

Interior angle of a Hexagon.

A hexagon has actually 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 angle of a rectangle

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

n = 4

Measure the each interior 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 interior angle =180° * (5 – 2)/5

=180° * 3/5

= 108°

Exterior angle of polygons

The exterior edge is the edge formed exterior a polygon between one side and prolonged side. The measure up of each exterior angle of a continual polygon is offered by;

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

One vital property around a consistent polygon’s exterior angle is the the sum of the steps of the exterior angles of a polygon is constantly 360°.

Examples

Exterior edge of a triangle:

For a triangle, n = 3

Substitute.

Measure of each exterior edge = 360°/n

= 360°/3

= 120°

Exterior angle of a Pentagon:

n = 5

Measure of every exterior angle = 360°/n

= 360°/5

= 72°

NOTE: The internal angle and also exterior edge formulas only occupational for continuous polygons. Irregular polygon have different interior and also exterior measures of angles.

Let’s watch at more example problems about interior and also exterior angle of polygons.

Example 1

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

Calculate the size of edge x in the polygon.

Solution

For a polygon v 6 sides, n = 6

the amount of inner angles =180° * (n – 2)

= 180° * (6 – 2)

= 180° * 4

= 720°

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

Simplify.

494° + x = 720°

Subtract 494° native both sides.

494° – 494° + x = 720° – 494°

x = 226°

Example 2

Find the exterior angle of a continual polygon through 11 sides.

Solution

n =11

The measure up 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°. Determine 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 worth of x is 20°.

Example 4

What is the name of a polygon whose internal angles room 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 political parties by 180°n.

140°n – 180°n = 180°n – 180°n – 360°

-40°n = -360°

Divide both political parties by -40°

n = -360°/-40°

= 9.

See more: How Much Is 17Cm In Inches ? Convert 17 Centimeters To Inches

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

Practice Questions

The first four inner angles of a pentagon space all, and also the 5th angle is 140°. Discover the measure up of the four angles.Find the measure of a polygon’s eight angles if the very first seven angles are 132° each.Calculate the angle of a polygon i m sorry are offered 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. Calculate the measure up of the angles.What is the name of a polygon having each internal angle as 135°?