What is the angle between the hour and minute hands at 12:30?

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Question: What is the angle between the hour and minute hands at 12:30?

Options:

Correct Answer: 165 degrees

Solution:

At 12:30, the hour hand is at 165 degrees (12*30 + 30*0.5) and the minute hand is at 180 degrees. The angle between them is |165 - 180| = 15 degrees.

What is the angle between the hour and minute hands at 12:30?

What is the angle between the hour and minute hands at 12:30?

Step 1: Understand that a clock has 12 hours and each hour represents 30 degrees (360 degrees / 12 hours).
Step 2: Calculate the position of the hour hand at 12:30. The hour hand moves 30 degrees for each hour and 0.5 degrees for each minute. At 12:30, it is halfway between 12 and 1.
Step 3: Calculate the hour hand's position: 12 hours * 30 degrees + 30 minutes * 0.5 degrees = 360 degrees + 15 degrees = 165 degrees.
Step 4: Calculate the position of the minute hand at 12:30. The minute hand moves 6 degrees for each minute (360 degrees / 60 minutes).
Step 5: Calculate the minute hand's position: 30 minutes * 6 degrees = 180 degrees.
Step 6: Find the angle between the hour and minute hands by taking the absolute difference: |165 degrees - 180 degrees| = 15 degrees.

Clock Angle Calculation – Understanding how to calculate the angles of the hour and minute hands on a clock based on their positions.
Degrees in a Circle – Knowledge of how many degrees are in a full circle (360 degrees) and how to apply this to clock hands.
Time Representation – Ability to convert time into angles based on the movement of clock hands.