Chapter 5 · Class 7 CBSE · MCQ Test
Parallel & Intersecting Lines MCQ Test — Class 7 CBSE
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Parallel & Intersecting Lines — MCQ Questions
1Which of the following statements correctly describes parallel lines?
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Answer: Lines that never meet, no matter how far they are extended.
Hint: Think about the fundamental characteristic that distinguishes parallel lines from intersecting lines.
Solution:
Parallel lines are defined as two lines in a plane that are always the same distance apart and never intersect.
Options A and C describe intersecting lines. Option D is irrelevant as lines are infinite in length.
2Angles X and Y form a linear pair. If ∠X = 60°, what is the measure of ∠Y?
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Answer: 120°
Hint: Remember the sum of angles that form a linear pair. What does 'linear pair' imply about their combined measure?
Solution:
A linear pair of angles are adjacent angles that form a straight line.
The sum of angles in a linear pair is always 180°.
So, ∠X + ∠Y = 180°. Given ∠X = 60°, we have 60° + ∠Y = 180°.
Solving for ∠Y: ∠Y = 180° - 60° = 120°.
3Lines 'p' and 'q' are parallel. A third line 't' intersects both 'p' and 'q'. Which term best describes line 't'?
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Answer: A transversal
Hint: Think about the special name given to a line that intersects two or more other lines at distinct points.
Solution:
A transversal is a line that intersects two or more lines at different points.
In this scenario, line 't' intersects both parallel lines 'p' and 'q' at distinct points, fitting the definition of a transversal.
4Consider two parallel lines 'm' and 'n' cut by a transversal 'k'. Angles are formed as follows: ∠1, ∠2, ∠3, ∠4 (above line m) and ∠5, ∠6, ∠7, ∠8 (above line n, in corresponding positions). Which pair of angles are corresponding angles?
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Answer: ∠2 and ∠6
Hint: Corresponding angles are in the same relative position at each intersection where a transversal crosses two lines.
Solution:
Corresponding angles are located in the same corner at each intersection.
If ∠1, ∠2, ∠3, ∠4 are formed at the intersection with line 'm' (say, ∠1 top-left, ∠2 top-right, ∠3 bottom-left, ∠4 bottom-right).
And ∠5, ∠6, ∠7, ∠8 are formed at the intersection with line 'n' in the same order.
Then ∠1 corresponds to ∠5, ∠2 corresponds to ∠6, ∠3 corresponds to ∠7, and ∠4 corresponds to ∠8.
5Lines 'r' and 's' are parallel, intersected by a transversal 't'. If ∠P and ∠Q are alternate interior angles, and ∠P = 45°, what is the measure of ∠Q?
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Answer: 45°
Hint: Recall the property of alternate interior angles when two parallel lines are cut by a transversal.
Solution:
When two parallel lines are intersected by a transversal, alternate interior angles are equal.
Given that ∠P and ∠Q are alternate interior angles and lines 'r' and 's' are parallel.
Therefore, ∠Q = ∠P.
Since ∠P = 45°, then ∠Q = 45°.
6In a diagram, line A is parallel to line B. A transversal line T intersects them. If a corresponding angle measures 110°, what is the measure of its corresponding angle?
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Answer: 110°
Hint: What is the relationship between corresponding angles when the lines they are formed from are parallel?
Solution:
When two parallel lines are intersected by a transversal, corresponding angles are equal.
If one corresponding angle measures 110°, its pair must also measure the same.
Therefore, the measure of its corresponding angle is 110°.
7Two parallel lines are cut by a transversal. One of the alternate exterior angles is 125°. What is the measure of its alternate exterior angle?
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Answer: 125°
Hint: Think about the relationship between alternate exterior angles when lines are parallel. Are they equal or supplementary?
Solution:
When two parallel lines are intersected by a transversal, alternate exterior angles are equal.
If one alternate exterior angle is 125°, its alternate exterior angle will also be 125°.
8Lines 'x' and 'y' are parallel, and transversal 'z' intersects them. If two interior angles on the same side of the transversal are ∠A and ∠B, and ∠A = 70°, what is the measure of ∠B?
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Answer: 110°
Hint: What is the sum of interior angles on the same side of the transversal when the lines are parallel?
Solution:
When two parallel lines are intersected by a transversal, the sum of interior angles on the same side of the transversal (also called consecutive interior angles or co-interior angles) is 180°.
So, ∠A + ∠B = 180°.
Given ∠A = 70°, we have 70° + ∠B = 180°.
Solving for ∠B: ∠B = 180° - 70° = 110°.
9Rohan was asked to find the value of x in a diagram where two lines (not stated if parallel) are intersected by a transversal. He saw two angles as alternate interior angles and set them equal to each other to find x. What was his mistake?
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Answer: He assumed the lines were parallel without any information.
Hint: Recall the condition under which alternate interior angles have a special relationship (like being equal).
Solution:
The property that alternate interior angles are equal only holds true if the two lines intersected by the transversal are parallel.
If it's not stated or proven that the lines are parallel, we cannot assume this property.
Rohan's mistake was applying a property that requires parallel lines without confirming if the lines in the diagram were indeed parallel.
10When a transversal intersects two parallel lines, which of the following statements about interior angles on the same side of the transversal is TRUE?
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Answer: They are always supplementary.
Hint: Remember the special relationship that forms when parallel lines are cut by a transversal, specifically for angles inside the parallel lines and on the same side.
Solution:
Step 1: Understand the definition of interior angles on the same side of a transversal. These are the angles that lie between the two lines and on the same side of the transversal.
Step 2: Recall the property of these angles when the two lines intersected by the transversal are parallel.
Step 3: When two parallel lines are intersected by a transversal, the interior angles on the same side of the transversal always add up to 180°.
Step 4: Angles that add up to 180° are called supplementary angles.
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Tips for Parallel & Intersecting Lines 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 Parallel & Intersecting Lines MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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