How many practice questions are available for Angle Relationships?

SparkEd Math offers 60+ practice questions for Angle Relationships 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 Angle Relationships content free on SparkEd Math?

Yes! All Angle Relationships 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 Angle Relationships differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Angle Relationships 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 Angle Relationships content aligned with the IB syllabus?

Yes, all Angle Relationships questions and lessons on SparkEd Math are fully aligned with the International Baccalaureate (MYP) (IB) syllabus for Class 7. The content follows the official curriculum structure and exam pattern.

Angle Relationships — Class 7 IB (2025-26)

About Angle Relationships — Class 7 IB

Explore complementary, supplementary, and vertically opposite angles with parallel lines. This topic is part of the IB Class 7 mathematics syllabus (chapter: Unit 5). 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 Angle Relationships

Unlocking Angles: The Basics of Turns and Lines
Crossing Paths: Vertically Opposite and Corresponding Angles
Hidden Angles: Alternate and Co-interior Relationships
Triangle Treasures: Angle Sum and Exterior Angles
Beyond Triangles: Angles in Quadrilaterals and Problem Solving

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

Angle Relationships — solved examples for Class 7 IB

Example 1easy

Angles around a point in a town square are formed by paths intersecting. If three angles measure 75°, 110°, and 90°, what is the measure of the fourth angle?

A)75°
B)85°
C)90°
D)100°

Step-by-step solution

The sum of angles around a point is 360°.
Add the given angles: 75° + 110° + 90° = 275°.
Subtract this sum from 360° to find the fourth angle: 360° - 275° = 85°.
$360° - (75° + 110° + 90°)$

Answer: 85°

Example 2medium

Three support beams meet at a central point on a circular platform in a new public park in Geneva. One angle formed between two beams measures 105°, and another angle is 120°. What is the measure of the third angle?

A)A. 115°
B)B. 125°
C)C. 130°
D)D. 135°

Step-by-step solution

Angles around a central point sum to 360°.
Sum of the two given angles = 105° + 120° = 225°.
To find the third angle, subtract the sum of the known angles from 360°.
$Third angle = 360° - 225°$
Third angle = 135°.

Answer: D. 135°

Example 3hard

Four angles meet at a point O in a complex gear system. The angles are: ∠AOB = (2x + 10)°, ∠BOC = (3x - 5)°, ∠COD = (x + 20)°, and ∠DOA = (4x - 25)°. Find the measure of ∠DOA.

A)A. 105°
B)B. 119°
C)C. 125°
D)D. 135°

Step-by-step solution

The sum of angles at a point is 360°. So, (2x + 10) + (3x - 5) + (x + 20) + (4x - 25) = 360.
Combine like terms: 10x + 0 = 360, which simplifies to 10x = 360.
Solve for x: x = 360 ÷ 10 = 36.
Substitute x = 36 into the expression for ∠DOA: ∠DOA = (4 × 36 - 25)° = (144 - 25)° = 119°.

Answer: B. 119°

Practice questions on Angle Relationships

Q1.easy
A straight road in Berlin is intersected by a pedestrian crossing. If one angle formed by the intersection on one side of the road is 132°, what is the measure of the adjacent angle on the straight road?
1. A)38°
2. B)48°
3. C)52°
4. D)62°
Show answer
Answer: 48°
Hint: Angles on a straight line always add up to a specific total. Think about a protractor.
Q2.easy
When two straight lines intersect, they form four angles. If one of the angles is 65°, what is the measure of the angle vertically opposite to it?
1. A)25°
2. B)65°
3. C)115°
4. D)180°
Show answer
Answer: 65°
Hint: Vertically opposite angles have a special relationship regarding their measures.
Q3.easy
In a city grid, two parallel streets, Elm Street and Oak Avenue, are crossed by a transversal road. If the angle formed at the upper-left intersection of Elm Street and the transversal is 110°, what is the measure of the corresponding angle at Oak Avenue?
1. A)70°
2. B)90°
3. C)110°
4. D)180°
Show answer
Answer: 110°
Hint: Think about the position of corresponding angles relative to the parallel lines and transversal.
Q4.medium
In the urban planning of a new district in Berlin, a straight main road is intersected by a pedestrian path. If one angle formed between the road and the path is (3x + 10)° and the adjacent angle on the straight road is (2x + 20)°, what is the value of x?
1. A)A. 30
2. B)B. 35
3. C)C. 40
4. D)D. 45
Show answer
Answer: A. 30
Hint: Angles on a straight line are supplementary, meaning they add up to 180°.
Q5.medium
Two straight laser beams cross each other in a physics experiment. If one angle formed is 105°, what is the measure of the angle vertically opposite to the adjacent angle on a straight line?
1. A)A. 75°
2. B)B. 85°
3. C)C. 105°
4. D)D. 115°
Show answer
Answer: A. 75°
Hint: First, find the adjacent angle on the straight line. Then, consider its vertically opposite angle.
Q6.medium
A designer is planning a pattern for a building facade in Dubai, using parallel lines. If a transversal line intersects two parallel lines, and an angle above the upper parallel line and to the left of the transversal is 130°, what is the measure of the angle below the lower parallel line and to the left of the transversal?
1. A)A. 130°
2. B)B. 120°
3. C)C. 50°
4. D)D. 60°
Show answer
Answer: A. 130°
Hint: Identify the relationship between the two angles described: they are corresponding angles.
Q7.hard
A straight beam of light passes through point P, creating three angles on one side: ∠APQ = (x + 10)°, ∠QPR = (2x - 20)°, and ∠RPS = (x + 30)°. Find the value of x.
1. A)A. 40
2. B)B. 35
3. C)C. 37.5
4. D)D. 42.5
Show answer
Answer: A. 40
Hint: Recall that angles on a straight line sum to 180°. Form an equation with the given algebraic expressions.
Q8.hard
Two straight lines, AB and CD, intersect at point E, similar to a crosswalk intersection in a European city. Which of the following statements must always be true?
1. A)A. ∠AEC + ∠DEB = 180°
2. B)B. ∠AEC and ∠AED are complementary.
3. C)C. If ∠AEC = 70°, then ∠CEB = 110°.
4. D)D. ∠AEC + ∠CEB + ∠BED = 360°
Show answer
Answer: C. If ∠AEC = 70°, then ∠CEB = 110°.
Hint: Recall the definitions of vertically opposite angles and angles on a straight line. Consider how these relationships apply to intersecting lines.
Q9.hard
Lines m and n are cut by a transversal t, resembling a road crossing parallel railway tracks. An angle in the upper-left position where t intersects m is (3x + 30)°. An angle in the lower-left position where t intersects n is (5x - 50)°. For lines m and n to be parallel, what must be the value of x?
1. A)A. 20
2. B)B. 30
3. C)C. 35
4. D)D. 40
Show answer
Answer: D. 40
Hint: For lines to be parallel, corresponding angles must be equal. Identify the corresponding angles in the given description.

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