Geometry Puzzle – Challenge 66

Challenge:

What is the degree between the hour hand and minute hand of a clock at 4:30?

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From question 64 we learned that an hour hand of a clock moves 30 degree in one hour. At 4:30, the hour hand of the clock has moved 135 degree. (4.5 × 30 = 135)
At 4:30, the minute hand has moved 180 degree. So, the angle between hour and minute hand of the clock equals:
180 to 135 = 45 degree

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Frequently Asked Questions

How do you solve clock angle problems?

Find where each hand points, measured in degrees from 12, then subtract. The minute hand moves 6° per minute, and the hour hand moves 30° per hour plus 0.5° per minute. At 4:30 the minute hand is at 6 × 30 = 180° and the hour hand is at 30 × 4 + 0.5 × 30 = 135°, so the angle between them is 45°.

What is the clock angle problem formula?

The angle between the hands at h hours and m minutes is |30h − 5.5m| degrees. If the result is over 180°, subtract it from 360° to get the smaller angle. For 4:30, |30 × 4 − 5.5 × 30| = |120 − 165| = 45°. The 5.5 comes from the minute hand’s 6° per minute minus the hour hand’s 0.5° per minute.

How do you find the angle between clock hands?

Work out the smaller angle first, then remember the hands also make a larger reflex angle around the other side. At 4:30 the smaller angle is 45°, so the reflex angle is 360° − 45° = 315°. Most questions want the smaller one, but read carefully. A common mistake is leaving the hour hand on the 4, which would give 60° instead of 45°.

What are some clock angle questions with solutions?

Try these with |30h − 5.5m|. At 3:15, |90 − 82.5| = 7.5°. At 9:00, |270 − 0| = 270°, so the smaller angle is 90°. At 2:20, |60 − 110| = 50°. At 6:00, the hands point opposite ways, 180° apart. Each one checks the same idea as the 4:30 puzzle: the hour hand keeps moving between hour marks.

Can class 6 students solve clock angle questions?

Yes. Clock angle questions only need the fact that a circle has 360°, so each hour mark is 360 ÷ 12 = 30° apart, plus a little multiplication. Sixth graders can solve the 4:30 puzzle by noting the hour hand is halfway between 4 and 5, which is 15° past the 4, so the hands are 45° apart.

Related Lessons You May Like

• How to find the area of rectangles
• How to find the perimeter of rectangles
• How to find complementary, supplementary, vertical, and adjacent angles
• How to solve angles and angle measure
• How to solve multi-step word problems

If your student enjoys puzzles like this, Geometry for Beginners dives into the same kinds of relationships inside a full curriculum. For the algebra you will lean on, Pre-Algebra for Beginners fills in the foundations gently.