NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Multiple Choice Questions
Question 4

Question.  4

Measures of the two angles between hour and minute hands of a clock at 9 O’clock are

(A)

60°, 300°

(B)

270°, 90°

(C)

75°, 285°

(D)

30°, 330°

Detailed Answer with Explanation:

Step-by-step explanation (beginner friendly)

  • At 9:00, the minute hand points at 12.
  • At 9:00, the hour hand points at 9.
  • Each number gap on the clock equals \(30^{\circ}\) because \(360^{\circ} \div 12 = 30^{\circ}\).
  • The hands are 3 number gaps apart: from 9 to 12 is 3 steps.
  • Smaller angle:
    \(3 \times 30^{\circ} = 90^{\circ}\)
  • The clock makes a full circle of
    \(360^{\circ}\)
  • Larger (reflex) angle:
    \(360^{\circ} - 90^{\circ} = 270^{\circ}\)

So, the two angles are \(90^{\circ}\) and \(270^{\circ}\).

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