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

Terms Related to Polygons

Interior and Exterior of the Polygon

Convex and Concave Polygons

Regular and Irregular 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


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.



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.



Share this page: What’s this?

Recent Articles

  1. Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

    Mar 02, 24 05:31 PM

    Fractions
    The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

    Read More

  2. Subtraction of Fractions having the Same Denominator | Like Fractions

    Mar 02, 24 04:36 PM

    Subtraction of Fractions having the Same Denominator
    To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numera…

    Read More

  3. Addition of Like Fractions | Examples | Worksheet | Answer | Fractions

    Mar 02, 24 03:32 PM

    Adding Like Fractions
    To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the com…

    Read More

  4. Comparison of Unlike Fractions | Compare Unlike Fractions | Examples

    Mar 01, 24 01:42 PM

    Comparison of Unlike Fractions
    In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a nu…

    Read More

  5. Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

    Feb 29, 24 05:12 PM

    Equivalent Fractions
    The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with re…

    Read More

Polygons - Worksheets

Worksheet on Polygon and its Classification

Worksheet on Interior Angles of a Polygon

Worksheet on Exterior Angles of a Polygon