Chapter 6 · Class 9 CBSE · MCQ Test
Lines & Angles MCQ Test — Class 9 CBSE
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Lines & Angles — MCQ Questions
1An angle measures 75°. What type of angle is its reflex angle?
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Answer: Reflex angle
Hint: Remember that a reflex angle is greater than 180° but less than 360°. Calculate the reflex angle first.
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.
2Which of the following statements is TRUE regarding complementary and supplementary angles?
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Answer: The sum of two supplementary angles is 180°.
Hint: Recall the definitions of complementary and supplementary angles and their respective sums.
Solution:
Complementary angles are two angles whose sum is 90°.
Supplementary angles are two angles whose sum is 180°.
A linear pair consists of two adjacent angles that are supplementary, but not all supplementary angles form a linear pair (they don't have to be adjacent).
3Two 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?
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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.
Solution:
The description states that ray QS stands on line PQ, meaning P, Q, S are collinear, and ∠PQS is a straight angle (180°).
Angles ∠PQR and ∠RQS are adjacent (they share a common vertex Q and a common arm QR).
Since their non-common arms (QP and QS) form a straight line, their sum is 180°.
Adjacent angles whose sum is 180° form a linear pair.
4If two lines intersect at a point, and one of the angles formed is 65°, what is the measure of its vertically opposite angle?
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Answer: 65°
Hint: Recall the property of vertically opposite angles formed when two lines intersect.
Solution:
When two lines intersect, they form two pairs of vertically opposite angles.
A key theorem states that vertically opposite angles are always equal.
Therefore, if one angle is 65°, its vertically opposite angle must also be 65°.
5Ravi was solving a problem where two lines AB and CD intersect at O. He concluded that ∠AOC + ∠BOC = 90°. What mistake did Ravi make?
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Answer: He incorrectly applied the linear pair axiom.
Hint: Consider the relationship between adjacent angles that form a straight line. What should their sum be?
Solution:
When lines AB and CD intersect at O, angles ∠AOC and ∠BOC are adjacent angles.
They form a linear pair along the line AB (or CD, depending on how they are viewed, but specifically on line AB).
According to the linear pair axiom, the sum of angles in a linear pair is 180°, not 90°.
Concluding their sum is 90° implies they are complementary, which is incorrect for a linear pair unless one of them is 0° and the other 90°, which is not the general case.
6In a diagram, two parallel lines 'm' and 'n' are intersected by a transversal 't'. If ∠1 and ∠2 are corresponding angles, which of the following statements is always true?
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Answer: ∠1 = ∠2
Hint: Recall the property of corresponding angles when parallel lines are cut by a transversal.
Solution:
When two parallel lines are intersected by a transversal, specific angle pairs have special relationships.
Corresponding angles are one such pair, located in the same relative position at each intersection.
The property of corresponding angles states that if lines are parallel, then corresponding angles are equal.
7Two parallel lines 'p' and 'q' are intersected by a transversal 'r'. If an alternate interior angle is 110°, what is the measure of the other alternate interior angle?
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Answer: 110°
Hint: Think about the relationship between alternate interior angles when lines are parallel.
Solution:
Alternate interior angles are formed on opposite sides of the transversal and between the two parallel lines.
A fundamental theorem states that if two parallel lines are intersected by a transversal, then each pair of alternate interior angles is equal.
Therefore, if one alternate interior angle is 110°, the other alternate interior angle must also be 110°.
8If two parallel lines are intersected by a transversal, what is the relationship between the interior angles on the same side of the transversal?
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Answer: They are always supplementary.
Hint: These angles are also sometimes called consecutive interior angles or co-interior angles. What is their sum?
Solution:
Interior angles on the same side of the transversal are located between the parallel lines and on the same side of the transversal.
When the lines are parallel, these angles are not equal unless both are 90°.
The property for parallel lines states that interior angles on the same side of the transversal are supplementary, meaning their sum is 180°.
9Consider two lines 'a' and 'b' and a transversal 'c'. Which of the following conditions is SUFFICIENT to prove that line 'a' is parallel to line 'b'?
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Answer: A pair of alternate exterior angles are equal.
Hint: Think about the converse theorems related to parallel lines. Which angle relationships *guarantee* parallelism?
Solution:
Vertically opposite angles are always equal, regardless of whether lines are parallel, so this doesn't prove parallelism.
A linear pair always sums to 180°, which is true for any intersecting line and doesn't prove parallelism between two distinct lines.
The converse of the alternate exterior angles theorem states that if a transversal intersects two lines such that a pair of alternate exterior angles is equal, then the two lines are parallel.
The sum of angles on a straight line is 180° is a basic axiom and does not establish parallelism.
10If line P is parallel to line Q, and line Q is parallel to line R, what can be concluded about lines P and R?
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Answer: Line P is parallel to line R.
Hint: This is a direct application of a fundamental theorem regarding lines parallel to the same line.
Solution:
This scenario describes a specific geometric property.
The theorem states: Lines which are parallel to the same line are parallel to each other.
Since P || Q and Q || R, it logically follows that P || R.
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Tips for Lines & Angles 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 Lines & Angles MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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