NCERT - Mathematics

Book: NCERT - Mathematics

Chapter: 3. Understanding Quadrilaterals

Subject: Maths - Class 8th

Q. No. 6 of Exercises 3.3

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6

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram

We know,

Sum of adjacent angles = 180°


∠A + ∠B = 180o


2∠A = 180o (∠A = ∠B)


∠A = 90o


∠B = ∠A = 90o


∠C = ∠A = 90o (Opposite angles of parallelogram)


∠D = ∠B = 90o (Opposite angles of parallelogram)


Hence, each angle of the parallelogram measures 90o


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Chapter Exercises

Exercises 3.1
Exercises 3.2
Exercises 3.3
Exercises 3.4

More Exercise Questions

1

Given a parallelogram ABCD. Complete each statement along with the definition property used.


(i)


(ii)


(iii)


(iv)

2

Consider the following parallelogram. Find the values of the unknowns x, y, z

(i)


(ii)


(iii)


(iv)


(v)

3

Can a quadrilateral ABCD be a parallelogram if


(i) ∠D + ∠B = 180°?


(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?


(iii) ∠A = 70° and ∠C = 65°?
4

Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure
5

The measures of two adjacent angles of a parallelogram are in the ratio 3: 2. Find the measure of each of the angles of the parallelogram
6

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram
7

The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them
8

The following figures GUNS and RUNS are parallelograms

Find x and y (Lengths are in cm)


(i)


(ii)

9

In the above figure both RISK and CLUE are parallelograms. Find the value of x.
10

Explain how this figure is a trapezium. Which of its two sides are parallel? (Fig 3.32)
11

Find in Fig 3.33 if

12

Find the measure of and if in Fig 3.34.


(If you find is there more than one method to find ?)