Question

The minute hand of this clock is shown in two positions. The minute hand first forms a 46° angle with the hour hand. It then forms an 84° angle with the hour hand.

How many degrees did the minute hand turn from its first position to its second position?

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The face of a clock. The hour hand points to the 9. The minute hand is rotated to two positions. In its first position, the minute hand is between 10 and 11 so that it forms a 46 degree angle with the hour hand. In its second position, the minute hand is between 11 and 12 so that it forms an 84 degree angle with the hour hand. The angle formed by the first and second position of the minute hand is labeled with a question mark.

Answer 1

To find the number of degrees the minute hand turned from its first position to its second position, we need to find the difference between the two angles formed by the minute and hour hands.

In the first position, the minute hand forms a 46° angle with the hour hand. Since the hour hand is pointing at 10 and the minute hand is between 10 and 11, we know that the hour hand has moved 1/6th of the way from 10 to 11, or 30°. Therefore, the angle between the hour hand and the 12:00 position is 120° + 30° = 150°. So the minute hand is 46° away from 150°, or 104°.

In the second position, the minute hand forms an 84° angle with the hour hand. Since the hour hand is pointing at 10 and the minute hand is between 11 and 12, we know that the hour hand has moved 1/2 of the way from 10 to 11, or 150°. So the minute hand is 84° away from 150°, or 234°.

To find the number of degrees the minute hand turned, we subtract the two angles: 234° - 104° = 130°.

Therefore, the minute hand turned 130° from its first position to its second position.