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
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