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CBSE 9th Standard Mathematics Lines and Angles Sample Question Papers Study Material - QB365 Set D

Published on: 29/10/2025

Question Set D

CBSE 9th Standard Mathematics Lines and Angles Sample Question Papers Study Material - QB365

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Std: 9th Standard CBSE - Mathematics

chapter: Lines and Angles - Sample Question Papers

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Questions:

Multiple Choice Question

8 x 1 = 8

The compliment of (\(90^{ 0 }\)-\(a^{ 0 }\)) is

(a)

\(-a^{ 0 }\)

(b)

\(90^{ 0 }\)+\(a^{ 0 }\)

(c)

\(90^{ 0 }\)-\(a^{ 0 }\)

(d)

\(a^{ 0 }\)

An angle which is greater than \(90^{ 0 }\) and less than \(180^{ 0 }\) is called

(a)

a right angle

(b)

a straight angle

(c)

an acute angle

(d)

an obtuse angle

Two angles whose sum is \(90^{ 0 }\) are called

(a)

Supplementary angles

(b)

complimentary angles

(c)

corresponding angles

(d)

alternate angles

A reflex angle

(a)

is greater than \(180^{ 0 }\) but less than \(360^{ 0 }\)

(b)

is exactly equal to \(180^{ 0 }\)

(c)

is exactly equal to \(90^{ 0 }\)

(d)

is greater than \(90^{ 0 }\) but less than \(180^{ 0 }\)

The sum of two complimentary angles is

(a)

\(180^{ 0 }\)

(b)

\(360^{ 0 }\)

(c)

\(90^{ 0 }\)

(d)

None of these

An obtuse angle

(a)

measures between \(0^{ 0 }\) and \(90^{ 0 }\)

(b)

is greater than \(90^{ 0 }\) but less than \(180^{ 0 }\)

(c)

is exactly equal to \(90^{ 0 }\)

(d)

is exactly equal to \(180^{ 0 }\)

An angle which measures between \(0^{ 0 }\) and \(90^{ 0 }\) is called

(a)

a straight angle

(b)

an acute angle

(c)

a right angle

(d)

an obtuse angle

How many types of angles are formed between the edges of plane surfaces?

(a)

Of different types

(b)

Of only one type

(c)

Of only two types

(d)

of only three types

Generic 3

1 x 3 = 3

In figure \(\angle \)PQR =\(\angle \)PRQ then prove that \(\angle \) PQS =\(\angle \)PRT

Generic 4

4 x 4 = 16

10.

In the figure below \(l_{ 1 }||l_{ 2 }\) and \(a_{ 1 }||a_{ 2 }\) find the value of x.

11.

If two lines are perpendicular to the same line prove that they are parallel to each other.

12.

In the given figure , two straight lines PQ and RS intersect each other at O
If \(\angle \)POT =\(75^{ 0 }\) Find the values of a,b,c

13.

Ray OE bisects \(\angle \)AOB and OF the ray opposite to OE Show that \(\angle \)FOB=\(\angle \)FOA

Generic 2

3 x 2 = 6

14.

ABCDE is a regular pentagon as shown in the given figure Find the values \(\angle x\angle y\angle z\)

15.

Find the supplement of \(\frac { 4 }{ 3 } \) of right angle

16.

Two complementary angles are such that two times the measure of one to three times the measure of the other .Find the measure of the largest angle.

1 Marks

5 x 1 = 5

17.

In the figure below, if \(\angle A+\angle B+\angle C+\angle D+\angle E+\angle F=k\) right angles, then what is the value of k?

18.

If a transversal intersects two parallel lines, then which of the pairs of angles is equal.

19.

Two supplementary angles are in ratio 2:7. Find the measure of angles.

20.

Write the angle which is one-fifth of its complement.

21.

What is the measure of an angle which is complement of itself?

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Answers Key:

Multiple Choice Question

8 x 1 = 8

Complement of (\(90^{ 0 }\)-\(a^{ 0 }\))
=\(90^{ 0 }\)-(\(90^{ 0 }\)-\(a^{ 0 }\))=\(a^{ 0 }\)

Definition of an obuse angle

Definition of complimentary angles

Definition of a reflex angle

Definition of complementary angles

Definition of an obtuse angle

Definition of an acute angle

(a)
Of different types

Generic 3

1 x 3 = 3

\(\therefore \)Ray QP stands on line ST
\(\therefore \) \(\angle \)PQS +\(\angle \)PQR = \(180^{ 0 }\)
|Linear Pair Axiom
Ray RP stands on line ST
\(\therefore \) \(\angle \)PRQ +\(\angle \)PRT= \(180^{ 0 }\)
| Linear Pair Axiom
From (1) and (2) we obtain
\(\angle \)PQS+\(\angle \)PQR =\(\angle \)PRQ +\(\angle \)PRT
\(\Rightarrow \)\(\angle \) PQS =\(\angle \)PRT
\(\therefore \) \(\angle \)PQR=\(\angle \)PRQ(Given)

Generic 4

4 x 4 = 16

10.

\(\angle \)1=4x+15 | Corresponding angles
2x=180-\(\angle \)1 |Corresponding angles
\(\Rightarrow \) 2x=\(180^{ 0 }\) -(4x+15)
\(\Rightarrow \) 2x=165-4x
\(\Rightarrow \) 6x=165 \(\Rightarrow \)\(x=\frac { 165 }{ 6 } =27\frac { 1^{ 0 } }{ 2 } \)

11.

Let the two lines m and n each be perpendicular to the same line L

Then,
\(\angle \)1=\(90^{ 0 }\)
\(\angle \)2=\(90^{ 0 }\)
\(\angle \)1=\(\angle \)2
But these angles form a pair of equal corresponding angles
\(\therefore \) m||n

12.

\(\therefore \) ROS is a line
\(\therefore \) 4b+\(75^{ 0 }\)+b=\(180^{ 0 }\)
\(\Rightarrow 5b=180^{ 0 }-75^{ 0 }=105^{ 0 }\)
\(\Rightarrow \) b=\(\frac { 105^{ 0 } }{ 5 } =21^{ 0 }\)
2c=\(75^{ 0 }\)+b
|Vertically opposite angles
\(\Rightarrow 2c=75^{ 0 }+21^{ 0 }\)
\(\Rightarrow 2c=96^{ 0 }\)
\(\Rightarrow \)\(c=\frac { 96^{ 0 } }{ 2 } =48^{ 0 }\)
a=4b
|Vertically opposite angkes
\(\Rightarrow a=4X21^{ 0 }=84^{ 0 }\)
Thus \(a=84^{ 0 },b=21^{ 0 },c=48^{ 0 }\)

13.

\(\angle \)FOB+\(\angle \)BOE=\(180^{ 0 }\) ...(1)
| Linear pair Axiom
\(\angle \)FOA+\(\angle \)AOE=\(180^{ 0 }\) .. (2)
| Linear Pair Axiom
From (1) and (2)
\(\angle \)FOB+\(\angle \)BOE=\(\angle \) FOA+\(\angle \)AOE ....(3)
But \(\angle \)BOE=\(\angle \)AOE
\(\therefore \) From (3)
\(\Rightarrow \) \(\angle \)FOB=\(\angle \)FOA

Generic 2

3 x 2 = 6

14.

\(36^{ 0 },36^{ 0 },72^{ 0 }\)

15.

\(\frac{4}{3}\) of a right angle=\(\frac{4}{3}\times90^o=120^o\)
(Sum of supplementary angles is 180^o)
Supplement of 120^o=180^o-120^o=60^o

16.

\(54^{ 0 }\)

1 Marks

5 x 1 = 5

17.

()
In \(\triangle ABC,\)
\(\angle A+\angle B+\angle C=180^o\)
Also, in \(\triangle DEF,\)
\(\angle D+\angle E+\angle F=180^o\)
\(\therefore \angle A+\angle B+\angle C+\angle D+\angle E+\angle F=360^o\)
=4 X 90^o
Hence,k=4 right angles.