Unit 5 · Class 7 IB MYP · MCQ Test
Angle Relationships MCQ Test — Class 7 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Angle Relationships — MCQ Questions
1Angles 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?
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Answer: 85°
Hint: Remember that the sum of angles around a point is a full circle.
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°)
2A 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?
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Answer: 48°
Hint: Angles on a straight line always add up to a specific total. Think about a protractor.
Solution:
Angles on a straight line sum to 180°.
Subtract the known angle from 180° to find the adjacent angle: 180° - 132° = 48°. — 180° - 132°
3When 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?
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Answer: 65°
Hint: Vertically opposite angles have a special relationship regarding their measures.
Solution:
Vertically opposite angles are formed when two straight lines intersect.
A key property of vertically opposite angles is that they are always equal in measure.
Therefore, if one angle is 65°, its vertically opposite angle is also 65°.
4In 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?
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Answer: 110°
Hint: Think about the position of corresponding angles relative to the parallel lines and transversal.
Solution:
When two parallel lines are intersected by a transversal, corresponding angles are in the same relative position at each intersection.
Corresponding angles are equal in measure.
Therefore, if the angle at Elm Street is 110°, the corresponding angle at Oak Avenue is also 110°.
5Two parallel tracks for a high-speed train are crossed by a maintenance path. If an interior angle on one side of the path is 55°, what is the measure of its alternate interior angle?
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Answer: 55°
Hint: Alternate interior angles are found between the parallel lines but on opposite sides of the transversal.
Solution:
When two parallel lines are intersected by a transversal, alternate interior angles are located between the parallel lines and on opposite sides of the transversal.
Alternate interior angles are always equal in measure.
Thus, if one interior angle is 55°, its alternate interior angle is also 55°.
6Imagine two parallel electrical wires running across a field, connected by a diagonal support wire. If one co-interior angle formed by the support wire and the top electrical wire is 70°, what is the measure of the other co-interior angle with the bottom wire?
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Answer: 110°
Hint: Co-interior angles are on the same side of the transversal and between the parallel lines. What is their sum?
Solution:
When two parallel lines are intersected by a transversal, co-interior (or consecutive interior) angles are on the same side of the transversal and between the parallel lines.
Co-interior angles are supplementary, meaning their sum is 180°.
To find the other co-interior angle, subtract the known angle from 180°: 180° - 70° = 110°. — 180° - 70°
7Which statement about parallel lines intersected by a transversal is TRUE?
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Answer: Corresponding angles are always equal.
Hint: Review the definitions and properties of the angle pairs formed when a transversal cuts parallel lines.
Solution:
Let's examine each option:
A: This is false. Right angles can be formed if the transversal is perpendicular.
B: This is false. Alternate exterior angles are equal, not supplementary.
C: This is true. Corresponding angles are indeed always equal when lines are parallel.
D: This is false. Co-interior angles always sum to 180° (they are supplementary).
8A triangular roof truss in a building in Sydney has angles measuring 45° and 60°. What is the measure of the third angle in the truss?
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Answer: 75°
Hint: Recall the fundamental property of the sum of angles inside any triangle.
Solution:
The sum of interior angles in any triangle is always 180°.
Add the two known angles: 45° + 60° = 105°.
Subtract this sum from 180° to find the third angle: 180° - 105° = 75°. — 180° - (45° + 60°)
9A student, Leo, was asked to find the value of x in a diagram where two angles, (x + 20)° and 100°, are vertically opposite. Leo wrote: x + 20 + 100 = 180, so x = 60. What mistake did Leo make?
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Answer: He should have set the angles equal to each other.
Hint: Think about the definition and property of vertically opposite angles.
Solution:
Vertically opposite angles are equal in measure, not supplementary (sum to 180°) or angles on a point (sum to 360°).
Leo incorrectly assumed they sum to 180°, which applies to angles on a straight line or co-interior angles.
The correct approach is to set the expressions equal: x + 20 = 100. — x + 20 = 100
10A photographer is setting up a tripod. One leg forms an angle of 70° with the ground. If the other two legs are splayed symmetrically, and the angle between them at the top is vertically opposite to the angle formed by the first leg and the ground, what is the angle between the other two legs?
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Answer: 70°
Hint: Focus on the relationship described: vertically opposite angles.
Solution:
The problem states that the angle between the other two legs at the top is vertically opposite to the angle formed by the first leg and the ground (70°).
Vertically opposite angles are always equal in measure.
Therefore, the angle between the other two legs is also 70°.
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Tips for Angle Relationships MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Angle Relationships MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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