Sum of the Interior Angles of a Polygon
We will learn how to find the sum of the interior angles of a polygon having n sides.
We know that if a polygon has ‘n’ sides, then it is divided into (n – 2) triangles.
We also know that, the sum of the angles of a triangle = 180°.
Therefore, the sum of the angles of (n – 2) triangles = 180 × (n – 2)
= 2 right angles × (n – 2)
= 2(n – 2) right angles
= (2n – 4) right angles
Therefore, the sum of interior angles of a polygon having n sides is (2n – 4) right angles.
Thus, each interior angle of the polygon = (2n – 4)/n right angles.
Now we will learn how to
find the find the sum of interior angles of different polygons using the
formula.
|
Name |
Figure |
Number of Sides |
Sum of interior angles (2n - 4) right angles |
|
Triangle |
 |
3 |
(2n - 4) right angles = (2 × 3 - 4) × 90° = (6 - 4) × 90° = 2 × 90° = 180° |
|
Quadrilateral |
 |
4 |
(2n - 4) right angles = (2 × 4 - 4) × 90° = (8 - 4) × 90° = 4 × 90° = 360° |
|
Pentagon |
 |
5 |
(2n - 4) right angles = (2 × 5 - 4) × 90° = (10 - 4) × 90° = 6 × 90° = 540° |
|
Hexagon |
 |
6 |
(2n - 4) right angles = (2 × 6 - 4) × 90° = (12 - 4) × 90° = 8 × 90° = 720° |
|
Heptagon |
 |
7 |
(2n - 4) right angles = (2 × 7 - 4) × 90° = (14 - 4) × 90° = 10 × 90° = 900° |
|
Octagon |
 |
8 |
(2n - 4) right angles = (2 × 8 - 4) × 90° = (16 - 4) × 90° = 12 × 90° = 1080° |
Solved examples on sum of the interior angles of a polygon:
1. Find the sum of the measure of interior angle of a polygon having 19 sides.
Solution:
We know that the sum of the interior angles of a polygon is (2n - 4) right angles
Here, the number of sides = 19
Therefore, sum of the interior angles = (2 × 19 – 4) × 90°
= (38 – 4) 90°
= 34 × 90°
= 3060°
2. Each interior angle of a regular polygon is 135 degree then find the number of sides.
Solution:
Let the number of sides of a regular polygon = n
Then the measure of each of its interior angle = [(2n – 4) × 90°]/n
Given measure of each angle = 135°
Therefore, [(2n – 4) × 90]/n = 135
⇒ (2n – 4) × 90 = 135n
⇒ 180n – 360 = 135n
⇒ 180n - 135n = 360
⇒ 45n = 360
⇒ n = 360/45
⇒ n = 8
Therefore the number of sides of the regular polygon is 8.
● Polygons
Polygon and its Classification
Interior and Exterior of the Polygon
Number of Triangles Contained in a Polygon
Angle Sum Property of a Polygon
Problems on Angle Sum Property of a Polygon
Sum of the Interior Angles of a Polygon
Sum of the Exterior Angles of a Polygon
7th Grade Math Problems
8th Grade Math Practice
From Sum of the Interior Angles of a Polygon to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Division of Whole Numbers |Relation between Dividend, Divisor Quotient
Mar 05, 25 03:36 PM
Relation between Dividend, Divisor, Quotient and Remainder is. Dividend = Divisor × Quotient + Remainder. To understand the relation between dividend, divisor, quotient and remainder let us follow the… -
Multiplication of Whole Numbers | Whole Numbers|Multiplication|Numbers
Mar 05, 25 03:29 PM
Multiplication of whole numbers is the sort way to do repeated addition. The number by which any number is multiplied is known as the multiplicand. The result of the multiplication is known as the pro… -
12 Times Table | Read and Write Multiplication Table of 12|Times Table
Mar 05, 25 02:29 PM
In 12 times table we will learn how to read and write multiplication table of 12. We read twelve times table as: One time twelve is 12 Two times twelve are 24 Three times twelve are 36 -
Adding 1-Digit Number | Understand the Concept one Digit Number
Mar 05, 25 03:08 AM
Understand the concept of adding 1-digit number with the help of objects as well as numbers. -
Subtraction of Whole Numbers | Whole Number |Subtract One Large Number
Mar 04, 25 12:20 PM
Subtraction of whole numbers is discussed in the following two steps to subtract one large number from another large number: Step I: We arrange the given numbers in columns, ones under ones, tens unde…
● Polygons - Worksheets
Worksheet on Polygon and its Classification
Worksheet on Interior Angles of a Polygon
Worksheet on Exterior Angles of a Polygon
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.