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Angles Quiz - CBSE Class 9 Mathematics

Free practice quiz: 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 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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Types of angles

  • Angles are named by size: acute is less than a right angle, obtuse lies between right and straight.
  • Perpendicular lines meet at right angles. A straight angle is a straight line. Reflex angles exceed a straight angle.
Acute angle
\[0^\circ < x < 90^\circ\]
Right angle
\[x = 90^\circ\]
Obtuse angle
\[90^\circ < x < 180^\circ\]
Straight and reflex angles
\[\text{straight: } x = 180^\circ,\ \text{reflex: } 180^\circ < x < 360^\circ\]

Common mistake: Calling a right angle acute or obtuse. A right angle is exactly a right angle, neither acute nor obtuse.

Complementary and supplementary angles

  • Two angles are complementary if they add to a right angle. They are supplementary if they add to a straight angle.
  • Angles in a linear pair are supplementary. Vertically opposite angles are always equal.
Complementary
\[a + b = 90^\circ\]
Supplementary or linear pair
\[a + b = 180^\circ\]
Two equal supplementary angles
\[2a = 180^\circ \Rightarrow a = \frac{180^\circ}{2}\]
Vertically opposite angles
\[\angle 1 = \angle 3\]

Common mistake: Mixing up the two words. Complement goes with the right angle, supplement goes with the straight angle.

Triangle angle sum and exterior angle

  • The three interior angles of any triangle add up to a straight angle.
  • An exterior angle equals the sum of the two interior opposite angles. In a right triangle, the other two angles are complementary.
Angle sum property
\[\angle A + \angle B + \angle C = 180^\circ\]
Exterior angle property
\[\text{Exterior } \angle = \angle A + \angle B\]
Right triangle (right angle at C)
\[\angle A + \angle B = 90^\circ\]

Common mistake: Adding the exterior angle to all three interior angles. It equals only the sum of the two opposite interior angles.

Parallel lines and a transversal

  • When a transversal cuts two parallel lines, corresponding angles 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
\[\angle 4 + \angle 6 = 180^\circ\]

Common mistake: Assuming same-side interior angles are equal. They are supplementary. Only corresponding and alternate angles are equal.

Parallelogram and cyclic quadrilateral angles

  • In a parallelogram, opposite angles are equal and adjacent angles are supplementary.
  • In a cyclic quadrilateral, with all vertices on a circle, each pair of opposite angles is supplementary.
Parallelogram opposite angles
\[\angle A = \angle C,\ \angle B = \angle D\]
Parallelogram adjacent angles
\[\angle A + \angle B = 180^\circ\]
Cyclic quadrilateral
\[\angle A + \angle C = \angle B + \angle D = 180^\circ\]
Quadrilateral angle sum
\[\angle A + \angle B + \angle C + \angle D = 360^\circ\]

Common mistake: Saying opposite angles of a cyclic quadrilateral are equal. They add to a straight angle. Equality of opposite angles is a parallelogram property.

Exam tips

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

Sample questions

  1. What is the measure of a right angle?

    Show answer

    Answer: B. 90 degrees

    A right angle is defined as an angle that measures 90 degrees.

  2. If one angle of a triangle is 60 degrees and another is 70 degrees, what is the measure of the third angle?

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    Answer: A. 50 degrees

    The sum of the angles in a triangle is 180 degrees. So, 180 - 60 - 70 = 50 degrees.

  3. What type of angle can be formed by the hands of a clock at 3:00?

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    Answer: B. Right

    At 3:00, the hour hand points at 3 and the minute hand points at 12 forming a right angle (90 degrees).

  4. What is an angle's supplement if it measures 75 degrees?

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    Answer: A. 105 degrees

    The supplement of an angle is calculated as 180 degrees minus the angle's measure. Thus, 180 - 75 = 105 degrees.

  5. What is the angle formed between the hour hand and minute hand of a clock at 6:00?

    Show answer

    Answer: C. 180 degrees

    At 6:00, the hour hand points at 6 and the minute hand points at 12, creating a straight angle of 180 degrees.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. Which of the following angles is acute?
  2. What is the sum of the angles in a triangle?
  3. What type of angle is 120 degrees?
  4. If two angles are supplementary and one measures 110 degrees, what is the measure of the other angle?
  5. In a right triangle, if one of the angles is 30 degrees, what is the other non-right angle?
  6. In a parallelogram, what can be said about opposite angles?
  7. What is the exterior angle of a triangle if the two internal angles are 70 degrees and 60 degrees?
  8. Which statement is true about complementary angles?
  9. If two angles are equal and their sum is 180 degrees, what is the measure of each angle?
  10. What type of angle is formed at the intersection of two perpendicular lines?
  11. If an angle measures 150 degrees, what type of angle is it?
  12. In a cyclic quadrilateral, the sum of the opposite angles is:
  13. If the measure of one angle in a right angle is 36 degrees, what is the measure of its complement?
  14. A transversal intersects two parallel lines, forming angles of 40 degrees and x degrees on one side. What is the value of x?

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