At half-past three, what is the angle between the hands of a clock?

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## Brainteaser answer

First, a quick estimate. The short hand points across to the three, and the long hand points straight down to the 6. The angle is about 90 degrees, but there’s a more accurate answer.

At three o’clock, the short hand points to the three, but by half past, it’s pointing half-way between the three and the four.

There are 12 numbers on a clock face and 360 degrees in a circle, so we can calculate the angle between two numbers that are next to each other:

360 ÷ 12 = 30 degrees

At half past three, the short hand has moved halfway between the three and the four, which is 15 degrees from the three. Since it’s 90 degrees from the three to the six, it must be 90 – 15 = 75. That means the answer is 75 degrees from the short hand to the long hand.

As a circle has 360 degrees, there’s a second answer. If you measure the big angle, 360 – 75 = 285, so 285 degrees is also correct!

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