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 definition or property used.

**(i)** AD = ………

**(ii)** ∠DCB = …………….

**(iii)** OC = ……………….

**(iv)** m∠DAB + m∠CDA = …………..

**Solution.**

**(i)** AD = BC

Opposite sides of a parallelogram are equal

**(ii)** ∠DCB = ∠DAB

Opposite angles of a parallelogram are equal

**(iii)** OC = OA

∵ Diagonals of a parallelogram bisect each other

**(iv)** m∠DAB + m∠CDA = 180°

∵ Adjacent angles of a parallelogram are supplementary.

**Question 2.**

Consider the following parallelo¬grams. Find the values of the unknowns x, y, z.

**Solution.**

**(i)** y = 100°

Opposite angles of a parallelogram are equal

x + 100° = 180°

Adjacent angles in a parallelogram are supplementary

⇒ x = 180° – 100°

⇒ x = 80°

⇒ z – x = 80°

Opposite angles of a parallelogram are of equal measure

**(ii)** x + 50° = 180°

Adjacent angles in a parallelogram are supplementary

⇒ x = 180° – 50° = 130°

⇒ y = x = 130°

The opposite angles of a parallelogram are of equal measure

180° – z = 50°

Opposite angles of a parallelogram are of equal measure

⇒ z = 180° – 50° = 130°

**(iii)** x = 90°

Vertically opposite angles are equal

x + y + 30° = 180°

By angle sum property of a triangle

⇒ 90° + y + 30° = 180°

⇒ 120° + y = 180°

⇒ y = 180° – 120° = 60° z + 30° + 90° – 180°

By angle sum property of a triangle

z = 60°

**(iv)** y = 80°

Opposite angles of a parallelogram are of equal measure

x + 80° = 180°

Adjacent angles in a parallelogram are supplementary

⇒ x = 180° – 80°

⇒ x = 100°

⇒ 180°-2+ 80°= 180°

Linear pair property and adjacent angles in a parallelogram are supplementary.

z = 80°

**(v)** y = 112°

Opposite angles of a parallelogram are equal

x + y + 40° = 180°

By angle sum property of a triangle

⇒ x + 112° + 40° = 180°

⇒ x + 152° = 180°

⇒ x = 180°- 152°

⇒ x = 28°

z = x = 28°.

Alternate interior angles

**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)** Can be, but need not be

**(ii)** No: in a parallelogram, opposite sides are equal; but here, AD ≠ BC.

**(iii)** No: in a parallelogram, opposite angles are of equal measure; but here ∠A ≠ ∠C.

**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 kite, for 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 the two adjacent angles be 3x° and 2x°.

Then,

3x° + 2x° = 180°

∴ Sum of the two adjacent angles of a parallelogram is 180°

⇒ 5x° = 180°

⇒ \({ x }^{ \circ }=\frac { { 180 }^{ \circ } }{ 5 } \)

⇒ x° = 36°

⇒ 3x° = 3 x 36° = 108°

and

2x° = 2 x 36° = 72°.

Since, the opposite angles of a parallelogram are of equal measure, therefore the measures of the angles of the parallelogram are 72°, 108°, 72°, and 108°.

**Question 6.**

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

**Solution.**

Let the two adjacent angles of a parallelogram be x° each.

Then,

x° + x° = 180°

∴ Sum of the two adjacent angles of a parallelogram is 180°.

⇒ 2x° = 180°

⇒ \({ x }^{ \circ }=\frac { { 180 }^{ \circ } }{ 2 } \)

⇒ x° = 90°.

Since the opposite angles of a parallelogram are of equal measure, therefore the measure of each of the angles of the parallelogram is 90°, i.e., each angle of the parallelogram is a right angle.

**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.**

x = 180° – 70° = 110°

Linear pair property and the opposite angles of a parallelogram are of equal measure.

∵ HOPE is a || gm

∴ HE || OP

and HP is a transversal

∴ y = 40°

alternate interior angles

40° + z + x = 180°

The adjacent angles in a parallelogram are supplementary

⇒ 40° + z + 110° = 180°

⇒ z + 150° = 180°

⇒ z = 180° – 150°

⇒ z = 30°.

**Question 8.**

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

**(i)**

**(ii)**

**Solution.**

**(i)**

**For Figure GUNS**

Since the opposite sides of a parallelogram are of equal length, therefore,

⇒ 3x = 18

⇒ \(x=\frac { 18 }{ 3 } =6\)

and, 3y – 1 = 26

⇒ 3y = 26 + 1

⇒ 3y = 27

\(y=\frac { 27 }{ 3 } =9\)

Hence, x = 6; y = 9.

**(ii)**

**For Figure RUNS**

Since the diagonals of a parallelogram bisect each other, therefore,

⇒ x + y = 16 …(1)

and, y + 7 = 20 …(2)

From (2),

⇒ y – 20 – 7 = 13

Putting y = 13 in (1), we get

⇒ x + 13 = 16 ⇒ x = 16 – 13 = 3.

Hence, x = 3; y = 13.

**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 is parallel?

**Solution.**

∵ ∠KLM + ∠NML = 80° + 100° = 180°

∴ KL || NM

∵ The sum of consecutive interior angles is 180°

∴ Figure KLMN is a trapezium.

Its two sides \(\overline { KL } \) and \(\overline { NM } \) are parallel.

**Question 11.**

Find m∠C in the figure, if \(\overline { AB } \) || \(\overline { DC } \).

**Solution.**

∵ \(\overline { AB } \) || \(\overline { DC } \)

∴ m∠C + m∠B = 180°

∵ The sum of consecutive interior angles is 180°

m∠C+ 120° = 180°

⇒ m∠C = 180° – 120° = 60°.

**Question 12.**

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

**Solution.**

∵ \(\overline { SP } \) || \(\overline { RQ } \)

∴ m∠P+m∠Q = 180°

∵ The sum of consecutive interior angles is 180°

⇒ m∠P + 130° = 180°

⇒ m∠P = 180° – 130°

⇒ m∠P = 50°

Again, m∠R + m∠S = 180°

∵ The sum of consecutive interior angles is 180°

⇒ 90° + m Z S = 180°

⇒ m∠S = 180° – 90° = 90°

Yes; there is one more method of finding m∠P if m∠R is given and that is by using the angle sum property of a quadrilateral.

We have,

m∠P + m∠Q + m∠R + m∠S = 360°

⇒ m∠P + 130° + 90° + 90° = 360°

⇒ m∠P + 310° = 360°

⇒ m∠P = 360° – 310° = 50°.

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