Subscribe to our YouTube channel for the latest videos, updates, and tips.


Angle Sum Property of a Polygon

We will learn about the interior angle sum property of a polygon.

The sum of interior angles of a polygon can also be obtained without using the angle sum formula.

In the adjoining figure of a triangle the sum of interior angles of a triangle is always 180°.

i.e. for ∆ABC, ∠BAC + ∠ABC + ∠ACB = 180°

i.e. ∠A + ∠B + ∠C = 180°

Sum of Interior Angles of a Triangle

In the adjoining figure of a quadrilateral ABCD, if diagonal BD of the quadrilateral is drawn, the quadrilateral will be divided into two triangles i.e. ∆ABD and ∆BDC.

Since, the sum of interior angles of a triangle is 180°.

Therefore, in ∆ABD, ∠ABD+ ∠BDA + ∠DAB = 180°

and, in ∆BDC, ∠BDC + ∠DCB + ∠CBD = 180°


Sum of Interior Angles of a Quadrilateral

Adding we get;

∠ABD+ ∠BDA + ∠DAB + ∠BDC + ∠DCB + ∠CBD = 180° + 180°

⇒ (∠ABD + ∠CBD) + ∠DAB + (∠BDC + ∠BDA) + ∠DCB = 360°

⇒ ∠ABC + ∠DAB + ∠ADC + ∠DCB = 360°

⇒ ∠B + ∠A + ∠D + ∠C = 360°


In the adjoining figure of a pentagon ABCDE, on joining AC and AD of the pentagon is divided into three triangles ∆ABC, ∆ACD and ∆ADE.

Since, the sum of the interior angles of the triangles is 180°

Therefore, the sum of interior angles of the pentagon ABCDE = Sum of interior angles of (∆ABC + ∆ACD + ∆ADE)

= 180° + 180° + 180°

= 540°

Sum of Interior Angles of a Pentagon

In the adjoining figure of a hexagon ABCDE, on joining AC, AD and AE, the given hexagon is divided into four triangles i.e. ∆ABC, ∆ACD, ∆ADE and ∆AEF.

The sum of the interior angles of the hexagon ABCDEF = sum of the interior angles of (∆ABC + ∆ACD + ∆ADE + ∆AEF)

= 180° + 180° + 180° + 180°

= 720°

Sum of Interior Angles of a Hexagon

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 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.



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.




Share this page: What’s this?

Recent Articles

  1. How to Find the Average? | What Does Average Mean? | Definition

    May 15, 25 06:05 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  2. Worksheet on Rounding Off Number | Rounding off Number | Nearest 10

    May 15, 25 05:12 PM

    In worksheet on rounding off number we will solve 10 different types of problems. 1. Round off to nearest 10 each of the following numbers: (a) 14 (b) 57 (c) 61 (d) 819 (e) 7729 2. Round off to

    Read More

  3. Worksheet on Rounding Decimals | Questions Related to Round a Decimal

    May 15, 25 11:52 AM

    Worksheet on Rounding Decimals
    The worksheet on rounding decimals would be really good for the students to practice huge number of questions related to round a decimal. This worksheet include questions related

    Read More

  4. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 14, 25 03:01 PM

    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More

  5. Rounding Off to the Nearest Whole Number | Nearest 10, 100, and 1000

    May 13, 25 03:43 PM

    Nearest Ten
    Here we will learn how to rounding off to the nearest whole number?

    Read More

Polygons - Worksheets

Worksheet on Polygon and its Classification

Worksheet on Interior Angles of a Polygon

Worksheet on Exterior Angles of a Polygon