Clock Angle Puzzles Quiz: Hands, Degrees and Time

The hour hand creeps forward half a degree every minute, which is why many clock puzzles trick people, and this clock angle puzzles quiz walks through the logic. Play 10 online questions on how fast each hand moves, the formula 30H minus 5.5M, angles at 3:15, 12:30 and 9:45, how often the hands overlap and how many right angles happen each day.

Start Clock Angle Puzzles Quiz

🎯 Daily Trivia Challenge • 🧠 10 Questions • ⏱️ 150 Seconds

Question 1 / 10 Time: 150s

Minute
How many degrees does the minute hand move each minute?
Hour
How many degrees does the hour hand move each minute?
Three
What is the angle between the hands at exactly 3:00?
Quarter
What is the angle between the hands at 3:15?
Formula
Which formula gives the angle at H hours and M minutes?
Half
What is the angle at 12:30?
Nine
What is the angle at 9:45?
Overlap
How many times do the hands overlap in 12 hours?
First
Roughly when do the hands first overlap after 12:00?
Right
How many times a day do the hands form a right angle?

Explanations: answer key for all 10 questions

Q1: How many degrees does the minute hand move each minute?
Answer: 6
It travels 360 degrees in 60 minutes.
Q2: How many degrees does the hour hand move each minute?
Answer: 0.5
It travels 30 degrees each hour.
Q3: What is the angle between the hands at exactly 3:00?
Answer: 90 degrees
Each hour mark is 30 degrees apart.
Q4: What is the angle between the hands at 3:15?
Answer: 7.5 degrees
The hour hand has moved 7.5 degrees past the 3.
Q5: Which formula gives the angle at H hours and M minutes?
Answer: The absolute value of 30H minus 5.5M
Take 360 minus the result if it exceeds 180.
Q6: What is the angle at 12:30?
Answer: 165 degrees
The hour hand is 15 degrees past 12.
Q7: What is the angle at 9:45?
Answer: 22.5 degrees
The hour hand is 22.5 degrees past the 9.
Q8: How many times do the hands overlap in 12 hours?
Answer: 11
They overlap every 65 and 5/11 minutes.
Q9: Roughly when do the hands first overlap after 12:00?
Answer: About 1:05 and 27 seconds
It is 65 and 5/11 minutes after noon.
Q10: How many times a day do the hands form a right angle?
Answer: 44
That is 22 times every 12 hours.

Clock Angle Puzzles Quiz – Hands, Degrees and Time

Clock angle puzzles ask for the angle between the hour and minute hands. The minute hand moves 6 degrees per minute, while the hour hand moves 0.5 degrees per minute, which most people forget.

A handy formula is the absolute value of 30H minus 5.5M, where H is the hour and M the minutes. If the result is over 180 degrees, subtract it from 360 to get the smaller angle. At 3:15 the answer is 7.5 degrees, not zero.

The hands overlap 11 times in 12 hours, every 65 and 5/11 minutes, and form right angles 44 times a day. These puzzles appear in aptitude tests and train careful reasoning.

What This Quiz Teaches

Puzzle fans and math students will enjoy these questions.

How fast each hand moves
How to use the formula
Which times are tricky
How often hands overlap
How often right angles occur

Did You Know?

At 6:00 the hands form a straight line.
Hands point in opposite directions 11 times every 12 hours.
Digital clocks avoid this puzzle entirely.
Interview tests often include clock problems.
Drawing a sketch helps solve them.