Math Problem Statement

At 8:00, what is the angle between the hour and minute hands of the clock?

Solution

The image contains a question in Gujarati asking about the angle between the hour and minute hands of a clock at 8:00. The provided options are:

  • A) 120°
  • B) 230°
  • C) 180°
  • D) 80°

Let's solve this:

At 8:00, the hour hand is at the 8, and the minute hand is at the 12. Each number on the clock represents 30 degrees (since 360/12=30360^\circ / 12 = 30^\circ).

  • The hour hand at 8 is 8×30=2408 \times 30^\circ = 240^\circ from the 12 o'clock position.
  • The minute hand at 12 is at 0 degrees.

The difference between the two hands is: 2400=240240^\circ - 0^\circ = 240^\circ However, since the clock is circular, we take the smaller angle, which is: 360240=120360^\circ - 240^\circ = 120^\circ

So, the correct answer is A) 120°.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What is the angle between the hands at 3:00?
  2. How does the hour hand's position change over time?
  3. What is the formula to calculate the angle between the hands of a clock at any given time?
  4. How would the answer change if the time was 8:30 instead of 8:00?
  5. Can the angle between clock hands ever be more than 180 degrees?

Tip: Always subtract the calculated angle from 360° if the angle is more than 180° to find the smaller angle between clock hands.

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Math Problem Analysis

Mathematical Concepts

Clock angles
Geometry

Formulas

Angle between hour and minute hands = |(30 * hour - 5.5 * minutes)|
Angle of each hour = 360° / 12

Theorems

Basic properties of angles in circles

Suitable Grade Level

Grades 5-7