Angles in a clock: a. The hands of a clock make different angles at different times. At 1 o'clock, the angle between the hands is 30°. Why? b. What will be the angle at 2 o'clock? And at 4 o'clock? 6 o'clock? c. Explore other angles made by the hands of a clock.
A clock face is a circle of 360° divided into 12 hours. Each hour division equals 360° ÷ 12 = 30°. At 1 o'clock, the hour hand points at 1 and the minute hand points at 12, separated by one hour division, hence 30°.
At 2 o'clock: ° = 60°. At 4 o'clock: ° = 120°. At 6 o'clock: ° = 180° (straight angle).
At 3 o'clock: 90° (right angle). At 5 o'clock: 150°. At 9 o'clock: 270° or reflex angle of 90°. At 12 o'clock: 0° (hands overlap).
Explanation
(a) The full circle of 360° is divided into 12 equal parts on a clock face. (b) Multiply the hour number by 30° to find the angle between the hands. (c) Students can explore various times and calculate corresponding angles.