**Class 9 Maths Chapter 6 Lines and Angles MCQs **are given here online with correct answers. Students can practise these objective questions and test their problem-solving skills. All the multiple-choice questions are based on the latest CBSE syllabus and NCERT curriculum. Solving these chapter-wise problems will help students to score good marks. Also, check Important Questions for Class 9 Maths.

## MCQs on Class 9 Maths Chapter 6 Lines and Angles

Below are the MCQs for Chapter 6 Lines and Angles of 9th Standard. Each question has four options, among which one is the correct answer. Cross-check your answers with the one provided here.

**1) A line joining two endpoints is called:**

a. Line segment

b. A ray

c. Parallel lines

d. Intersecting lines

Answer:** a**

**2) An acute angle is:**

a. More than 90 degrees

b. Less than 90 degrees

c. Equal to 90 degrees

d. Equal to 180 degrees

Answer:** b**

**3) A reflex angle is:**

a. More than 90 degrees

b. Equal to 90 degrees

c. More than 180 degrees

d. Equal to 180 degrees

Answer:** c**

**4) A straight angle is equal to:**

a. 0°

b. 90°

c. 180°

d. 360°

Answer:** c**

**5) Two angles whose sum is equal to 180° are called:**

a. Vertically opposite angles

b. Complementary angles

c. Adjacent angles

d. Supplementary angles

Answer:** d**

**6) Intersecting lines cut each other at:**

a. One point

b. Two points

c. Three points

d. Null

Answer:** a**

Explanation: Two lines always intersect each other at one point.

**7) Two parallel lines intersect at:**

a. One point

b. Two points

c. Three points

d. Null

Answer:** d**

Explanation: If two lines are parallel to each other, they don’t intersect each other.

**8) If two lines intersect each other, then the vertically opposite angles are:**

a. Equal

b. Unequal

c. Cannot be determined

d. None of the above

Answer:** a**

Explanation: If two lines intersect each other, then the angles formed at the point of intersection are vertically opposite angles and are equal.

**9) In the figure below, which of the following are corresponding angle pairs?**

a. ∠p and ∠q

b. ∠p and ∠w

c. ∠p and ∠x

d. ∠p and ∠z

Answer:** b**

**10) If AB || CD, EF ⊥ CD and ∠GED = 135° as per the figure given below. **

**The value of ∠AGE is:**

a. 120°

b. 140°

c. 90°

d. 135°

Answer:** d**

Explanation: Since AB || CD and GE is transversal.

Given, ∠GED = 135°

Hence, ∠GED = ∠AGE = 126° (Alternate interior angles)

**11) An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is**

(a) 37 ½°

(b) 72 ½°

(c) 75°

(d) 52 ½°

Answer: **d**

Explanation:

The exterior angle of triangle = 105°

Let the interior angles be “x”.

By using, exterior angle theorem, Exterior angle = Sum of interior opposite angles

Therefore, 105° = x+x

2x = 105°

x = 52 ½°

**12) If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be **

(a) 50°

(b) 65°

(c) 145°

(d) 155°

Answer: **d**

Explanation:

Assume a triangle ABC, such that ∠BAC=130°

Also, the bisectors of ∠B and ∠C meet at O.

To find: ∠BOC

In a triangle △ABC,

∠BAC+∠ABC+∠ACB=180°

By using the angle sum property of the triangle,

130°+∠ABC+∠ACB=180°

∠ABC+∠ACB=50°

½ (∠ABC+∠ACB)=25°

Since OB and OC bisect ∠ABC and ∠ACB

∠OBC+ ∠OCB=25°

Now, consider △OBC,

∠OBC+ ∠OCB+∠BOC=180°

25°+∠BOC=180°

∠BOC=155°

**13) If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3, then the greater of the two angles is**

(a) 54°

(b) 108°

(c) 120°

(d) 136°

Answer: **b**

Explanation: Consider the following figure,

Here, line AB is parallel to the line CD and t is the transversal.

Here, ∠1 and ∠2 are on the same side of the transversal. Hence, ∠1: ∠2 = 2:3

Let ∠1 = 2x and ∠2 = 3x.

Therefore, ∠1+∠2 = 180° (If a transversal intersects two parallel lines, each pair of consecutive angles are supplementary)

On substituting ∠1 = 2x and ∠2 = 3x in the above equation, we get

2x+3x = 180°

5x = 180°

x = 180°/5 = 36°

Hence, 3x >2x. It means ∠2 >∠1

The value of ∠2 = 3(36°) = 108°

**14) If one angle of a triangle is equal to the sum of the other two angles, then the triangle is**

(a) a right triangle

(b) an isosceles triangle

(c) an equilateral triangle

(d) an obtuse triangle

Answer: **a**

Explanation: If one angle of a triangle is equal to the sum of the other two angles, then the triangle is a right triangle. We know that the sum of interior angles of a triangle is equal to 180°. In the right triangle, one angle should be equal to 90°, and the remaining two angles are acute angles, and their sum is equal to 90°.

**15) The angles of a triangle are in the ratio 5 : 3: 7. The triangle is**

(a) a right triangle

(b) an acute-angled triangle

(c) an obtuse-angled triangle

(d) an isosceles triangle

Answer: **b**

Explanation: If the angles are in the ratio of 5:3:7, then a triangle is an acute angle triangle.

We know that the sum of the interior angles of a triangle is 180°

Therefore, 5x+3x+7x = 180°

15x = 180°

x = 180°/15 = 12°

Thus, 5x = 5(12°) =60°

3x = 3(12°) =36°

7x = 7(12°) =84°

Since all the angles are less than 90°, the triangle is an acute angle triangle.

**16) Angles of a triangle are in the ratio 2: 4 : 3. The smallest angle of the triangle is**

(a) 20°

(b) 40°

(c) 60°

(d) 80°

Answer: **b**

Explanation:

We know that the sum of the interior angles of a triangle is 180°

Given that, the angles of a triangle are in the ratio of 2:4:3

Hence, 2x+4x+3x = 180°

9x = 180°

x= 20°

Therefore,

2x = 2(20) = 40°

4x = 4(20) = 80°

3x = 3(20) = 60°

Hence, the angles are 40°, 80° and 60°.

Therefore, the smallest angle of a triangle is 40°.

**17) In the given figure, POQ is a line. The value of x is**

(a) 20°

(b) 25°

(c) 30°

(d) 35°

Answer: **a**

Explanation:

Given that POQ is a line. Hence, POQ = 180°

Therefore, 40°+4x+3x = 180°

7x = 180°-40°

7x = 140°

x = 140°/7

x = 20°

Hence, the value of x is 20°.

**18) In the given figure, , if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to**

(a) 85°

(b) 110°

(c) 135°

(d) 145°

Answer: **d**

Explanation: Given that, AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°.

To find: ∠QRS.

∠SRB=∠CQP=60° (or)

∠QRA =∠RQD=25°

Therefore, ∠ARS+∠SRB=180°

∠ARS = 180°- 60°

∠ARS = 120°

Hence, ∠QRS = ∠ARS+∠QRA = 120°+25°

∠QRS = 145°

**19) An obtuse angle is **

(a) Less than 90°

(b) Greater than 90°

(c) Equal to 90°

(d) Equal to 180°

Answer:** b**

Explanation: An obtuse angle is an angle that is greater than 90°

**20) In the given figure, if OP||RS, ∠OPQ = 110° and ∠QRS = 130°, then ∠PQR is equal to**

(a) 40°

(b) 50°

(c) 60°

(d) 70°

Answer: **c**

Explanation:

Now, consider the figure,

Using, OP || RS, we know that

∠RWV = 180°- 130°

Hence, ∠RWV = 50°

Since opposite angles of intersecting lines are equal,

∠PWQ = ∠RWV = 50°

For line OP

∠OQP + θ = 180°

θ = 180° – ∠OPQ = 180° − 110°

θ = 70°

Now, by using the fact, that the sum of interior angles of a triangle is 180°, we can write

∠PQR + θ + ∠PWQ = 180°

∠PQR = 180°- θ – ∠PWQ = 180°- 70°- 50°

∠PQR = 180° − 120°

∠PQR = 60°

Hence, ∠PQR is equal to 60°.

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