Subscribe to our YouTube channel for the latest videos, updates, and tips.
Home | About Us | Contact Us | Privacy | Math Blog
Problems on Angle Sum Property of a Polygon
We will learn how to solve the problems on angle sum property of a polygon having 'n' sides. We know, the sum of 3 angles of a triangle is 180°.
1. Find the sum of all the interior angle of a polygon having 29 sides.
Solution:
We know that sum of all the interior angle in a polygon = (n - 2) × 180°
Here, n = 29
Therefore, the sum of all interior angles = (29 – 2) × 180°
= 27 × 180°
= 4860°.
2. If the sum of the measure of the interior angle of polygon is 3240, find the number of sides of the polygon.
Solution:
Let the number of sides of the polygon be n.
The sum of the interior angles = (2n – 4) right angles
But given sum of the interior angles = 3240
Therefore, (2n – 4) × 90° = 3240
⇒ 2n – 4 = 3240/90
⇒ 2n – 4 = 36
⇒ 2n = 36 + 4
⇒ 2n = 40
⇒ n = 40/2
⇒ n = 20
Therefore, the number sides of the polygon is 20.
3. Find the sum of interior angles of a decagon.
Solution:
We know, a decagon have 10 sides.
Therefore, n = 10
Sum of interior angles = (2n - 4) × 90°
= (2 × 10 - 4) × 90°
= (20 - 4) × 90°
= 16 × 90°
= 1440°
Therefore, the sum of interior angles of a decagon is 1440°.
4. Sum of all interior angles of a polygon is 3060°. How many sides does the polygon have?
Solution:
We know that sum of all the interior angles of a polygon = (n - 2) × 180°
According to the problem, we have
(n - 2) ×180 = 3060
⇒ (n - 2) = 3060/180
⇒ n – 2 = 17
⇒ n = 17 + 2
⇒ n = 19
Therefore, the polygon have 19 sides.
● 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 Problems on Angle Sum Property 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
-
5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math
Jul 11, 25 02:14 PM
In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl… -
Construction of a Circle | Working Rules | Step-by-step Explanation |
Jul 09, 25 01:29 AM
Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be… -
Combination of Addition and Subtraction | Mixed Addition & Subtraction
Jul 08, 25 02:32 PM
We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add -
Addition & Subtraction Together |Combination of addition & subtraction
Jul 08, 25 02:23 PM
We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and… -
5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet
Jul 08, 25 09:55 AM
A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known
● 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.