How many practice questions are available for Lines and Angles?

SparkEd Math offers 60+ practice questions for Lines and 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 and Angles content free on SparkEd Math?

Yes! All Lines and 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 and Angles differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Lines and 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 and Angles content aligned with the Olympiad syllabus?

Yes, all Lines and Angles questions and lessons on SparkEd Math are fully aligned with the Mathematical Olympiad Preparation (Olympiad) syllabus for Class 7. The content follows the official curriculum structure and exam pattern.

Lines and Angles — Class 7 Olympiad (2025-26)

About Lines and Angles — Class 7 Olympiad

Explore angle pairs, parallel lines with transversals, and solve multi-step angle-finding problems. This topic is part of the Olympiad Class 7 mathematics syllabus (chapter: Module 7). On this page you can practice 58 questions across three difficulty levels — 20 easy, 20 medium, and 18 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.

Lines and Angles — solved examples for Class 7 Olympiad

Example 1easy

If two distinct lines intersect, how many points of intersection can they have?

A)A) 0
B)B) 1
C)C) 2
D)D) Infinitely many

Step-by-step solution

By definition, two distinct lines can share at most one common point.
If they shared more than one point, they would cease to be distinct lines and would instead be the same line.

Answer: B) 1

Example 2medium

An angle is such that its complement is one-fourth of its supplement. What is the measure of the angle?

A)60°
B)75°
C)30°
D)45°

Step-by-step solution

Let the angle be x. Its complement is (90° - x) and its supplement is (180° - x).
According to the problem, (90° - x) = (1/4) × (180° - x).
Multiply both sides by 4: 4(90° - x) = 180° - x. This simplifies to 360° - 4x = 180° - x.
Rearranging terms, we get 3x = 180°, so x = 60°.

Answer: 60°

Example 3hard

Three distinct lines AB, CD, EF intersect at a point O. Given that ∠AOC = (3x - 20)°, ∠EOD = (x + 70)°, and ∠FOB = (2x + 10)°. Find the value of ∠COE.

A)85°
B)90°
C)95°
D)100°

Step-by-step solution

Since AB and CD are straight lines intersecting at O, ∠AOC and ∠BOD are vertically opposite. Thus, ∠BOD = (3x - 20)°.
Since CD is a straight line, ∠COE + ∠EOD = 180° (linear pair). Given ∠EOD = (x + 70)°, so ∠COE = 180° - (x + 70)° = (110 - x)°.
Since EF and AB are straight lines intersecting at O, ∠FOB and ∠EOA are vertically opposite. Given ∠FOB = (2x + 10)°, so ∠EOA = (2x + 10)°.
Angles on the straight line AB sum to 180°. So, ∠AOC + ∠COE + ∠EOA = 180°. Substitute the expressions: (3x - 20)° + (110 - x)° + (2x + 10)° = 180°. Simplify: 4x + 100 = 180 => 4x = 80 => x = 20.
Finally, calculate ∠COE: ∠COE = (110 - x)° = (110 - 20)° = 90°.

Answer: 90°

Practice questions on Lines and Angles

Q1.easy
An angle is 30° less than twice its supplement. What is the measure of the angle?
1. A)A) 70°
2. B)B) 110°
3. C)C) 50°
4. D)D) 130°
Show answer
Answer: B) 110°
Hint: Let the unknown angle be 'x'. Express its supplement in terms of 'x' and form an algebraic equation.
Q2.easy
In the given figure, two lines AB and CD intersect at O. If ∠AOC = (3x - 10)° and ∠BOD = (2x + 30)°, find the measure of ∠AOD.
1. A)A) 100°
2. B)B) 80°
3. C)C) 110°
4. D)D) 70°
Show answer
Answer: D) 70°
Hint: Remember that vertically opposite angles are equal. Once you find x, use the linear pair property to find ∠AOD.
Q3.easy
Three rays OA, OB, OC originate from a common point O. If ∠AOB = (2y + 5)°, ∠BOC = (3y - 15)° and A, O, C are collinear (form a straight line), what is the value of y?
1. A)A) 38
2. B)B) 25
3. C)C) 30
4. D)D) 35
Show answer
Answer: A) 38
Hint: If points A, O, C are collinear, then the angle ∠AOC forms a straight angle.
Q4.medium
Three distinct lines AB, CD, and EF intersect at a common point O. If ∠AOC = 45° and ∠FOD = 30°, what is the measure of ∠BOF?
1. A)45°
2. B)60°
3. C)75°
4. D)85°
Show answer
Answer: 75°
Hint: Identify pairs of vertically opposite angles and use the fact that angles on a straight line sum to 180° to find intermediate angles.
Q5.medium
In the given figure, if line 'l' is parallel to line 'm', and a transversal 't' intersects them, such that the interior angles on the same side of the transversal are (4x + 15)° and (2x + 45)°. Find the value of x.
1. A)10
2. B)20
3. C)30
4. D)40
Show answer
Answer: 20
Hint: Remember the property of interior angles on the same side of a transversal when two lines are parallel.
Q6.medium
In the figure, if line AB is parallel to line CD. A point P lies between the lines such that ∠AEP = 40° and ∠CPF = 30°. Find the measure of ∠EPF.
1. A)70°
2. B)60°
3. C)50°
4. D)40°
Show answer
Answer: 70°
Hint: Draw an auxiliary line through point P parallel to AB and CD. This will divide ∠EPF into two parts, each related to the given angles.
Q7.hard
Lines AB and CD are parallel. A transversal PQ intersects AB at R and CD at S. The bisector of ∠ARP and the bisector of ∠CSQ meet at T. If ∠RTS = 115°, find the measure of ∠ARS.
1. A)90°
2. B)105°
3. C)115°
4. D)125°
Show answer
Answer: 115°
Hint: Draw an auxiliary line through T parallel to AB (and CD). Use alternate interior angles and the angle sum property in the triangle formed by the bisectors.
Q8.hard
In ΔABC, point D is on BC. A line segment DE is drawn such that E is on AC and DE || AB. F is a point on AB such that DF is drawn. If ∠BAC = 70°, ∠ABC = 50°, and ∠EDF = 20°, find ∠DFC.
1. A)75°
2. B)80°
3. C)85°
4. D)90°
Show answer
Answer: 90°
Hint: First, find the angles in ΔABC. Then use the parallel line DE || AB to find angles involving DE. Finally, apply the angle sum property in ΔCDF.
Q9.hard
In ΔABC, the side BC is extended to D. The bisector of ∠ABC meets AC at E. The bisector of ∠ACD meets BE at F. If ∠BAC = 80°, find ∠BFC.
1. A)20°
2. B)30°
3. C)40°
4. D)50°
Show answer
Answer: 40°
Hint: This is a classic geometry result. Use the exterior angle property of a triangle and the angle bisector property. Express angles in terms of variables for ∠ABC and ∠ACB.

These are 9 of the 58 questions available for Lines and Angles. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.