Get exam-ready with Class 9 Maths Chapter 6 – Lines and Angles revision. Solve carefully designed MCQs to practice concepts and examples, and use fill-in-the-blanks to check your memory of the basics. With every question followed by its answer, you’ll find mistakes quickly and correct them on the spot.
Class 9th Maths Important MCQs with Answers from Chapter 6 – Lines and Angles
Question 1. Which of the following is NOT a type of angle?
a) Acute angle
b) Obtuse angle
c) Reflex angle
d) Parallel angle
Answer:
d) Parallel angle – There is no such type of angle in geometry.
Question 2. Two angles whose sum is 90° are called ___.
a) Supplementary
b) Complementary
c) Reflex
d) Adjacent
Answer:
b) Complementary – By definition, complementary angles add to 90°.
Question 3. Two angles whose sum is 180° are called ___.
a) Complementary
b) Supplementary
c) Reflex
d) Right angles
Answer:
b) Supplementary – By definition, supplementary angles add to 180°.
Question 4. If two angles form a linear pair, their sum is always ___.
a) 90°
b) 120°
c) 180°
d) 360°
Answer:
c) 180° – This follows from the Linear Pair Axiom.
Question 5. Vertically opposite angles formed when two lines intersect are always ___.
a) Equal
b) Unequal
c) Complementary
d) Supplementary
Answer:
a) Equal – By Theorem 6.1, vertically opposite angles are equal.
Question 6. If two lines are parallel, then alternate interior angles are ___.
a) Supplementary
b) Equal
c) Reflex
d) Linear pair
Answer:
b) Equal – Axiom of alternate interior angles.
Question 7. The distance between two parallel lines is always ___.
a) Zero
b) Equal everywhere
c) Unequal everywhere
d) Changing with transversal
Answer:
b) Equal everywhere – The perpendicular distance remains the same.
Question 8. If a ray stands on a line, the adjacent angles so formed add up to ___.
a) 90°
b) 180°
c) 270°
d) 360°
Answer:
b) 180° – By Axiom 6.1, sum is 180°.
Question 9. The converse of the linear pair axiom is also true: If the sum of two adjacent angles is 180°, their ___ form a line.
a) Bisectors
b) Common arms
c) Non-common arms
d) Vertices
Answer:
c) Non-common arms – Axiom 6.2 states this.
Question 10. The measure of an angle formed by a perpendicular to a line is ___.
a) 0°
b) 45°
c) 90°
d) 180°
Answer:
c) 90° – Perpendicular means right angle.
Question 11. If two lines intersect, how many pairs of vertically opposite angles are formed?
a) 1
b) 2
c) 3
d) 4
Answer:
b) 2 – Each intersection gives two equal opposite pairs.
Question 12. If ∠POR : ∠ROQ = 5 : 7, then ∠POR = ___.
a) 75°
b) 85°
c) 90°
d) 105°
Answer:
a) 75° – Ratio with linear pair sum = 180°.
Question 13. If two parallel lines are cut by a transversal, then interior angles on the same side are always ___.
a) Equal
b) Supplementary
c) Reflex
d) Right
Answer:
b) Supplementary – Interior angles on the same side add to 180°.
Question 14. The sum of angles around a point is always ___.
a) 90°
b) 180°
c) 270°
d) 360°
Answer:
d) 360°
Question 15. If two lines are parallel to the same line, then they are ___ to each other.
a) Perpendicular
b) Intersecting
c) Parallel
d) Equal
Answer:
c) Parallel – Theorem 6.6 proves this.
Question 16. Two lines in a plane which never meet are called ___.
a) Intersecting lines
b) Parallel lines
c) Perpendicular lines
d) Skew lines
Answer:
b) Parallel lines – Defined as non-intersecting coplanar lines.
Question 17. In a transversal, corresponding angles are equal if and only if the lines are ___.
a) Intersecting
b) Perpendicular
c) Parallel
d) Non-parallel
Answer:
c) Parallel – Converse of corresponding angles axiom.
Question 18. Two lines in space that are not parallel and do not intersect are called ___.
a) Parallel
b) Skew
c) Intersecting
d) Perpendicular
Answer:
b) Skew – Non-coplanar, non-parallel lines.
Question 19. The sum of all angles formed on one side of a straight line is always ___.
a) 90°
b) 180°
c) 270°
d) 360°
Answer:
b) 180° – From the linear pair axiom.
Question 20. A reflex angle is greater than ___ but less than 360°.
a) 90°
b) 120°
c) 150°
d) 180°
Answer:
d) 180° – Reflex angles are more than 180° but less than 360°.
Question 21. If AB || CD and y : z = 3 : 7, then x = ___.
a) 36°
b) 54°
c) 72°
d) 90°
Answer:
c) 72° – From parallel line angle properties.
Question 22. If AB || CD, EF ⊥ CD and ∠GED = 126°, then ∠AGE = ___.
a) 36°
b) 44°
c) 54°
d) 64°
Answer:
a) 36° – By corresponding and interior angle relations.
Question 23. In the same problem, ∠GEF = ___.
a) 54°
b) 64°
c) 74°
d) 90°
Answer:
b) 64° – Derived by angle sum property.
Question 25. A reflex angle is greater than ___ but less than 360°.
a) 90°
b) 120°
c) 150°
d) 180°
Answer:
d) 180° – Reflex angles are more than 180° but less than 360°.
Question 25. If PQ || ST, ∠PQR = 110° and ∠RST = 130°, then ∠QRS = ___.
a) 100°
b) 110°
c) 120°
d) 140°
Answer:
a) 100° – Using parallel line angle properties.
Question 26. If AB || CD, ∠APQ = 50° and ∠PRD = 127°, then x = ___.
a) 43°
b) 53°
c) 63°
d) 77°
Answer:
b) 53° – Parallel line property applied.
Question 27. In the same problem, y = ___.
a) 47°
b) 53°
c) 63°
d) 77°
Answer:
d) 77° – Derived from supplementary relation.
Question 28. If two adjacent angles form a linear pair, each must be ___ to the other.
a) Complementary
b) Supplementary
c) Equal
d) Reflex
Answer:
b) Supplementary – They add to 180°.
Question 29. If two lines are cut by a transversal and a pair of alternate exterior angles are equal, the lines are ___.
a) Parallel
b) Perpendicular
c) Skew
d) Intersecting
Answer:
a) Parallel – By converse of alternate angle axiom.
Question 30. A straight angle measures ___.
a) 90°
b) 120°
c) 180°
d) 360°
Answer:
c) 180° – By definition.
Question 31. If one angle of a linear pair is 47°, then the other angle is ___.
a) 43°
b) 133°
c) 137°
d) 147°
Answer:
c) 133° – Since linear pair = 180°, other angle = 180° – 47°.
Question 32. If two parallel lines are cut by a transversal, then each pair of alternate interior angles are ___.
a) Equal
b) Complementary
c) Supplementary
d) Reflex
Answer:
a) Equal – Alternate interior angles are equal when lines are parallel.
Question 33. If two angles are supplementary and one is 2/3 of the other, then the smaller angle is ___.
a) 60°
b) 70°
c) 72°
d) 80°
Answer:
b) 70° – Let smaller = x, larger = 180 – x, solve x = 2/3(180 – x).
Question 34. If a transversal intersects two parallel lines, the sum of the pair of interior angles on the same side of transversal is ___.
a) 60°
b) 90°
c) 120°
d) 180°
Answer:
d) 180° – By interior angle property of parallel lines.
Question 35. Two lines are parallel if and only if a transversal gives rise to equal ___ angles.
a) Adjacent
b) Corresponding
c) Supplementary
d) Reflex
Answer:
b) Corresponding – Equality of corresponding angles proves parallelism.
Question 36. The sum of the three angles forming around a straight line at a point is always ___.
a) 90°
b) 120°
c) 180°
d) 360°
Answer:
c) 180° – Linear pair axiom generalised to multiple adjacent angles.
Fill in the blanks on Lines and Angles for Class 9 Maths
1. Two angles are said to be complementary if their sum is ___.
Answer:
90°
2. Two angles are said to be supplementary if their sum is ___.
Answer:
180°
3. If two adjacent angles form a linear pair, their sum is always ___.
Answer:
180°
4. When two lines intersect, the pair of opposite angles formed are called ___ angles.
Answer:
vertically opposite
5. Vertically opposite angles are always ___.
Answer:
equal
6. If a ray stands on a line, it forms two adjacent angles whose sum is ___.
Answer:
180°
7. If the sum of two adjacent angles is 180°, then their non-common arms form a ___.
Answer:
straight line
8. Two lines in a plane which do not meet are called ___ lines.
Answer:
parallel
9. If a transversal intersects two parallel lines, then each pair of corresponding angles are ___.
Answer:
equal
10. If a transversal intersects two parallel lines, then each pair of alternate interior angles are ___.
Answer:
equal
11. If a transversal intersects two parallel lines, then the interior angles on the same side of transversal are ___.
Answer:
supplementary
12. The sum of the angles around a point is always ___.
Answer:
360°
13. A straight angle is equal to ___.
Answer:
180°
14. An angle greater than 180° but less than 360° is called a ___ angle.
Answer:
reflex
15. Two lines which meet at right angles are called ___ lines.
Answer:
perpendicular
16. The sum of the two interior opposite angles of a triangle is equal to the ___ angle.
Answer:
exterior
17. If two parallel lines are cut by a transversal, each pair of alternate exterior angles are ___.
Answer:
equal
18. If two lines are parallel to the same line, then they are ___ to each other.
Answer:
parallel
19. The sum of two supplementary angles is always ___.
Answer:
180°
20. The sum of two complementary angles is always ___.
Answer:
90°
21. If ∠A and ∠B are complementary and ∠A = 40°, then ∠B = ___.
Answer:
50°
22. If two parallel lines are cut by a transversal and one angle is 70°, then its alternate interior angle is ___.
Answer:
70°
23. The sum of the three angles formed on one side of a straight line at a point is always ___.
Answer:
180°
24. If two lines intersect, the number of pairs of vertically opposite angles formed is ___.
Answer:
2
25. If ∠1 and ∠2 form a linear pair and ∠1 = 125°, then ∠2 = ___.
Answer:
55°
