NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.3 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.3.

- Understanding Quadrilaterals Class 8 Ex 3.1
- Understanding Quadrilaterals Class 8 Ex 3.2
- Understanding Quadrilaterals Class 8 Ex 3.4

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 3 |

Chapter Name |
Understanding Quadrilaterals |

Exercise |
Ex 3.3 |

Number of Questions Solved |
12 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.3

**Question 1.**

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

**(i)** AD = ………

**(ii)** ∠DCB = …………….

**(iii)** OC = ……………….

**(iv)** m∠DAB + m∠CDA = …………..

**Solution.**

**(i)** AD = BC : In a parallelogram, opposite sides are euqal.

**(ii)** ∠DCB = ∠DAB : In a parallelogram, opposite angles are equal.

**(iii)** OC = OA : The diagonals of a parallelogram bisect each other.

**(iv)** m∠DAB + m∠CDA = 180° : In a parallelogram, the stun of any two adjacent angles is 180°.

**Question 2.**

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

**Solution.**

**Question 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°?

**Solution.**

**(i)** If in a quadrilateral ABCD, ∠D + ∠B = 180°, then it is not necessary that ABCD is a parallelogram.

**(ii)** Since AD ≠ BC, i.e., the opposite sides are unequal, so ABCD is not a parallelogram.

**(iii)** Since ∠A ≠ ∠C, i.e., the opposite angles are unequal, so ABCD is not a parallelogram.

**Question 4.**

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

**Solution.**

A rough figure of a quadrilateral ABCD that is not a parallelogram has been drawn with exactly two opposite angles of equal measure such that ∠A – ∠C which is a kite as an example.

**Question 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.

**Solution.**

Let two adjacent angles A and B of ||gm ABCD be 3x and 2x respectively.

Since the adjacent angles of a parallelogram are supplementary.

Since the opposite angles are equal in a parallelogram, therefore,

∠C = ∠A = 108° and ∠D = ∠B = 72°

Hence, ∠A = 108°, ∠B = 72°, ∠C = 108° and ∠D = 72°.

**Question 6.**

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

**Solution.**

Let two adjacent angles A and B of parallelogram ABCD be x each.

Since the adjacent angles of a parallelogram are supplementary.

**Question 7.**

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

**Solution.**

Since HOPE is a parallelogram, therefore, HE || OP and HO || EP.

Now, HE || OP and transversal HO intersects them.

Hence, x = 110°, y = 40° and z = 30°

**Question 8.**

The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)

**Solution.**

**(i)** Since GUNS is a parallelogram, therefore, its opposite sides are equal.

**(ii)** In a parallelogram, diagonals bisect each other, therefore,

**Question 9.**

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

**Solution.**

**Question 10.**

Explain how this figure is a trapezium. Which of its two sides are parallel ?

**Solution.**

Since ∠KLM + ∠NML = 180° i.e., the pair of consecutive interior angles are supplmentary.

Therefore, KL || NM and so KLMN is a trapezium.

**Question 11.**

Find m∠C in the figure, if || .

**Solution.**

Since AB || DC and transversal BC intersects

them.

∠B + ∠C= 180°

[∵ Sum of interior angles is 180°]

⇒ 120°+ ∠C =180° A

⇒ ∠C = 180°- 120° = 60°

Hence, m∠C =60°

**Question 12.**

Find the measure of ∠P and ∠S, if || in the figure. (If you find mZ R, is there more than one method to find m∠P ?)

**Solution.**

Since SP || RQ and PQ is a transversal intersecting them at P and Q.

∴ ∠P + ∠Q =180°

[∵ Sum of interior angles is 180°]

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