How many practice questions are available for Lines & Angles?

SparkEd Math offers 60+ practice questions for Lines & Angles across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Lines & Angles content free on SparkEd Math?

Yes! All Lines & Angles content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Lines & Angles differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Lines & Angles problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Lines & Angles content aligned with the CBSE syllabus?

Yes, all Lines & Angles questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Lines & Angles — Class 9 CBSE (2025-26)

About Lines & Angles — Class 9 CBSE

Prove and apply theorems on linear pairs, vertically opposite angles, and parallel line transversals. This topic is part of the CBSE Class 9 mathematics syllabus (chapter: Chapter 6). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Lines & Angles

Introduction to Lines and Angles
Intersecting Lines and Transversals
Properties of Parallel Lines and Transversals
Converse Theorems and Triangle Angle Properties
Summary and Practice Preparation

Interactive lesson · about 15 minutes · checkpoint question after every unit

Lines & Angles — solved examples for Class 9 CBSE

Example 1easy

An angle measures 75°. What type of angle is its reflex angle?

A)Acute angle
B)Obtuse angle
C)Right angle
D)Reflex angle

Step-by-step solution

The reflex angle of a given angle 'x' is calculated as 360° - x.
For an angle of 75°, its reflex angle is 360° - 75° = 285°.
An angle that is greater than 180° and less than 360° is classified as a reflex angle.

Answer: Reflex angle

Example 2medium

An angle measures 280°. What type of angle is it?

A)A) Acute angle
B)B) Obtuse angle
C)C) Right angle
D)D) Reflex angle

Step-by-step solution

An acute angle is between 0° and 90°.
An obtuse angle is between 90° and 180°.
A right angle is exactly 90°.
A reflex angle is an angle greater than 180° but less than 360°. Since 280° is between 180° and 360°, it is a reflex angle.

Answer: D) Reflex angle

Example 3hard

Two lines AB and CD intersect at point O. If ∠AOC : ∠AOD = 2 : 7, what is the reflex angle ∠BOD?

A)280°
B)320°
C)300°
D)340°

Step-by-step solution

Angles ∠AOC and ∠AOD form a linear pair on line AB. Therefore, ∠AOC + ∠AOD = 180°.
Given ∠AOC : ∠AOD = 2 : 7. Let ∠AOC = 2x and ∠AOD = 7x. So, 2x + 7x = 180° => 9x = 180° => x = 20°.
Thus, ∠AOC = 2 × 20° = 40°.
∠BOD is vertically opposite to ∠AOC. So, ∠BOD = ∠AOC = 40°. The reflex angle ∠BOD = 360° - 40° = 320°.

Answer: 320°

Practice questions on Lines & Angles

Q1.easy
Which of the following statements is TRUE regarding complementary and supplementary angles?
1. A)Complementary angles always form a linear pair.
2. B)The sum of two complementary angles is 180°.
3. C)Supplementary angles add up to 90°.
4. D)The sum of two supplementary angles is 180°.
Show answer
Answer: The sum of two supplementary angles is 180°.
Hint: Recall the definitions of complementary and supplementary angles and their respective sums.
Q2.easy
Two angles, ∠PQR and ∠RQS, are adjacent. If a ray QS stands on a line PQ, and ∠PQS forms a straight angle, what can be concluded about ∠PQR and ∠RQS?
1. A)They are complementary angles.
2. B)They are vertically opposite angles.
3. C)They form a linear pair.
4. D)They are alternate interior angles.
Show answer
Answer: They form a linear pair.
Hint: Consider the definition of a linear pair: two adjacent angles whose non-common arms are opposite rays, forming a straight line.
Q3.easy
If two lines intersect at a point, and one of the angles formed is 65°, what is the measure of its vertically opposite angle?
1. A)25°
2. B)115°
3. C)65°
4. D)180°
Show answer
Answer: 65°
Hint: Recall the property of vertically opposite angles formed when two lines intersect.
Q4.medium
Two angles form a linear pair. If one angle measures (3x - 10)° and the other measures (2x + 30)°, what is the value of x?
1. A)A) 32
2. B)B) 36
3. C)C) 40
4. D)D) 44
Show answer
Answer: B) 36
Hint: Remember that angles forming a linear pair are supplementary, meaning their sum is 180°.
Q5.medium
In a figure, two lines AB and CD intersect at a point O. If ∠AOC = 40°, find the measure of ∠BOD and ∠AOD.
1. A)A) ∠BOD = 40°, ∠AOD = 140°
2. B)B) ∠BOD = 140°, ∠AOD = 40°
3. C)C) ∠BOD = 40°, ∠AOD = 50°
4. D)D) ∠BOD = 50°, ∠AOD = 140°
Show answer
Answer: A) ∠BOD = 40°, ∠AOD = 140°
Hint: Vertically opposite angles are equal, and angles on a straight line form a linear pair.
Q6.medium
Lines l and m are parallel, and t is a transversal. If ∠1 and ∠5 are corresponding angles, and ∠1 = (2x + 10)° and ∠5 = (3x - 20)°, find the measure of ∠1.
1. A)A) 70°
2. B)B) 60°
3. C)C) 50°
4. D)D) 40°
Show answer
Answer: A) 70°
Hint: Remember that when two parallel lines are cut by a transversal, corresponding angles are equal.
Q7.hard
In the given figure, lines PQ and RS intersect at point O. If ∠POR = (3x - 10)° and ∠QOS = (2x + 30)°, and ∠ROQ = y°, find the value of y. (Assume x and y are positive integers)
1. A)60°
2. B)70°
3. C)80°
4. D)90°
Show answer
Answer: 70°
Hint: Vertically opposite angles are equal. Also, angles forming a linear pair sum to 180°.
Q8.hard
Which of the following conditions is SUFFICIENT to prove that two distinct lines 'l' and 'm' are parallel when intersected by a transversal 't'?
1. A)The sum of interior angles on the same side of the transversal is 180°.
2. B)The corresponding angles are supplementary.
3. C)One pair of alternate interior angles are complementary.
4. D)One pair of interior angles on the same side of the transversal are equal.
Show answer
Answer: The sum of interior angles on the same side of the transversal is 180°.
Hint: Recall the converse theorems for parallel lines. Only one of these statements directly implies that the lines are parallel.
Q9.hard
In the figure, AB || CD and PQ is a transversal intersecting AB at P and CD at Q. If ∠APQ = (5x - 30)° and ∠PQD = (3x + 20)°, find the value of x.
1. A)25°
2. B)30°
3. C)35°
4. D)40°
Show answer
Answer: 25°
Hint: Identify the relationship between the given angles when two parallel lines are intersected by a transversal.

These are 9 of the 60 questions available for Lines & Angles. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.