Sum of Angles of a Quadrilateral



Sum of angles of a quadrilateral are discussed here. We have now two triangles in the below figure.

We know, the sum of the angles of a triangle = 180°

Since there are two triangles,

therefore, the sum of two triangles is 180° + 180° = 360°

Sum of Angles of a Quadrilateral




Note: The sum of the four angles is 360°.


For Example:

1. In a quadrilateral ABCD, ∠A = 100°, ∠B = 105° and ∠C = 70°, find ∠D.

Solution:

Here the sum of the four angles

or, ∠A + ∠B + ∠C + ∠D = 360°

We know, ∠A = 100°, ∠B = 105° and ∠C = 70°

or, 100° + 105° + 70° + ∠D = 360°

or, 275° + ∠D = 360°

∠D = 360° - 275°

Therefore, ∠D = 85°



2. Find the measure of the missing angles in a parallelogram, if ∠A = 70°.


missing angles in a parallelogram




Solution:

We know the opposite angles of a parallelogram are equal.

So, ∠C will also measure 70°

Sum of angles = 360°

∠A + ∠B + ∠C + ∠D = 360°

or, 70° + ∠B + 70° + ∠D = 360° (We know, ∠A = ∠C )

or, ∠B + ∠D + 140° = 360°

or, ∠B + ∠D = 360° - 140°

or, ∠B + ∠D = 220°

But ∠B = ∠D (Because opposites angles of a parallelogram are equal)

∠B = ∠D

= 220° ÷ 2

= 110°

Therefore, ∠B = 110°, ∠C = 70° and ∠ D = 110°

● Quadrilaterals.

Elements of a Quadrilateral.

Types of Quadrilaterals.

Parallel Lines.

Perpendicular Lines.

Construction of Perpendicular Lines by using a Protractor.

Sum of Angles of a Quadrilateral.

Worksheet on Quadrilateral.

Practice Test on Quadrilaterals.




5th Grade Geometry Page

5th Grade Math Problems

From Sum of Angles of a Quadrilateral 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. Divide by Repeated Subtraction | Division as Repeated Subtraction

    Jan 21, 25 09:09 AM

    Divide by Repeated Subtraction
    How to divide by repeated subtraction? We will learn how to find the quotient and remainder by the method of repeated subtraction a division problem may be solved.

    Read More

  2. Division Sharing and Grouping | Facts about Division | Basic Division

    Jan 21, 25 08:06 AM

    Sharing and Grouping
    We will learn division sharing and grouping. Share eight strawberries between four children. Let us distribute strawberries equally to all the four children one by one.

    Read More

  3. 3rd Grade Multiplication Worksheet | Grade 3 Multiplication Questions

    Jan 20, 25 02:31 PM

    3rd Grade Multiplication Riddle
    In 3rd Grade Multiplication Worksheet we will solve how to multiply 2-digit number by 1-digit number without regrouping, multiply 2-digit number by 1-digit number with regrouping, multiply 3-digit num…

    Read More

  4. 3rd Grade Math Worksheets |3rd Grade Math Sheets|3rd Grade Math Lesson

    Jan 20, 25 12:28 AM

    3rd Grade Math Worksheets
    3rd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students. Teachers and parents can also follow the worksheets to guide the students.

    Read More

  5. 3rd Grade Multiplication Word Problems Worksheet With Answers | Math

    Jan 19, 25 11:29 PM

    In 3rd Grade Multiplication Word Problems Worksheet we will solve different types of problems on multiplication, multiplication word problems on 3-digits number by 1-digit number and multiplication wo…

    Read More