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.
Mar 02, 24 05:31 PM
Mar 02, 24 04:36 PM
Mar 02, 24 03:32 PM
Mar 01, 24 01:42 PM
Feb 29, 24 05:12 PM
● 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.