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Lines and Angles Quiz - CBSE Class 9 Mathematics

Free practice quiz: Lines and Angles (CBSE Class 9 Mathematics). 19 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 9 Mathematics practice quiz has 19 multiple-choice questions on Lines and Angles, and 19 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Complementary, Supplementary and Linear Pairs

  • A full turn is 360°. A right angle is a quarter turn and a straight angle is a half turn.
  • Complementary angles add up to one right angle. Supplementary angles add up to one straight angle.
  • A linear pair is two adjacent angles on a straight line. They are always supplementary.
Right angle
\[\text{right angle} = \tfrac{1}{4}(360^\circ)\]
Straight angle
\[\text{straight angle} = \tfrac{1}{2}(360^\circ)\]
Complement of x
\[\text{complement} = \text{right angle} - x\]
Supplement of x
\[\text{supplement} = \text{straight angle} - x\]

Common mistake: Mixing up complement and supplement. Remember: complement means a right angle in total, supplement means a straight angle in total.

Vertically Opposite Angles

  • When two lines cross, the angles directly opposite each other are called vertically opposite angles.
  • Vertically opposite angles are always equal. Neighbouring angles at the crossing form linear pairs.
Lines AB and CD meet at O
\[\angle AOC = \angle BOD,\ \angle AOD = \angle BOC\]

Common mistake: Thinking adjacent angles at the crossing are equal. Only opposite angles are equal; adjacent ones are supplementary.

Parallel Lines and a Transversal

  • A transversal is a line that cuts two or more lines at different points.
  • If the lines are parallel, corresponding angles are equal and alternate interior angles are equal.
  • Interior angles on the same side of the transversal (co-interior angles) are supplementary.
Corresponding angles
\[\angle 1 = \angle 5\]
Alternate interior angles
\[\angle 3 = \angle 6\]
Co-interior angles
\[\angle 4 + \angle 6 = \text{straight angle}\]

Common mistake: Assuming co-interior angles are equal. They add up to a straight angle; only corresponding and alternate angles are equal.

Angle Sum of a Triangle

  • The three interior angles of any triangle add up to one straight angle.
  • An exterior angle equals the sum of the two interior opposite angles.
  • A triangle can have at most one right angle or one obtuse angle.
Angle sum property
\[\angle A + \angle B + \angle C = \text{straight angle}\]
Exterior angle property
\[\text{exterior } \angle = \angle A + \angle B\]
Angles in ratio form
\[x + kx + (x + m) = \text{straight angle}\]

Common mistake: Forgetting that all three angles must be included in the sum, or adding the exterior angle as a fourth interior angle.

Types of Triangles and Angles

  • Acute angle is less than a right angle; obtuse is more than a right angle but less than a straight angle.
  • A right triangle has one right angle. An isosceles triangle has a pair of equal angles opposite equal sides.
  • On a clock, the gap between neighbouring hour marks is one-twelfth of a full turn.
Clock: one hour gap
\[\frac{360^\circ}{12}\]
Angle between hands (n hour gaps)
\[n \times \frac{360^\circ}{12}\]

Common mistake: Calling a triangle with equal angles scalene. Equal angles mean equal opposite sides, so it is isosceles (or equilateral if all are equal).

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. If two lines intersect, how many pairs of vertically opposite angles are formed?

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    Answer: C. 2

    When two lines intersect, two pairs of vertically opposite angles are formed.

  2. Which angle is formed by the hands of a clock at 3:00?

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    Answer: A. 90 degrees

    At 3:00, the hands of the clock form a right angle (90 degrees).

  3. When a transversal cuts through two parallel lines, the interior angles on the same side of the transversal are:

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    Answer: B. Supplementary

    The interior angles on the same side of the transversal are supplementary, meaning they add up to 180 degrees.

  4. If angle A measures 50 degrees, what is the measure of its complement?

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    Answer: B. 40 degrees

    The complement of an angle measuring 50 degrees is 90 - 50 = 40 degrees.

  5. If angle A is 120 degrees, what is the measure of its supplement?

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    Answer: A. 60 degrees

    The supplement of an angle is calculated as 180 minus the angle. So, 180 - 120 = 60 degrees.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. What is the sum of the angles on a straight line?
  2. If two parallel lines are cut by a transversal, then which pairs of angles are always equal?
  3. What type of angles add up to 90 degrees?
  4. What type of angles add up to 180 degrees?
  5. In a triangle, if one angle is 90 degrees, what kind of triangle is it?
  6. What is true about the sum of all internal angles of a triangle?
  7. How many acute angles can a triangle have at maximum?
  8. Two angles are supplementary if the sum of their measures is:
  9. What is the complement of an angle measuring 65 degrees?
  10. What type of triangle has two equal angles?
  11. If two angles are equal and supplementary, what is the measure of each angle?
  12. A linear pair of angles are:
  13. What do you call the angles that are formed on opposite sides of a transversal intersecting two parallel lines?
  14. In triangle ABC, if angle A is twice angle B and angle C is 30 degrees greater than angle B, find all angles.

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