Thisactivity is around Analog clocks and the angles made by thehands the the clock. Friend can uncover out more about angles and how they"re measure on thepage Degrees(Angles).

You are watching: It’s 2 pm. how many degrees are in the angle between the hour and minute hand?

What is the angle between the hands of a clock at 1 o"clock?


in ~ 1 o"clock the minute hand(red) points to the 12 and also thehour hand (blue) points come the 1.So we require to find the angle betweenthe 12and the 1.

How countless of this angle space there in a complete turn?


There space 12 of them in a complete turn (360°), for this reason eachonemust be360°÷ 12= 30°

therefore the edge betweenthehandsof a clock in ~ 1 o"clock is30°.


It doesn"tmatter even if it is we are talking around 1 am or 1pm, the prize is precisely the same for both.The angle between the hands at1 o"clock could additionally be provided as the reflex edge 330°,but us willalways give the smaller sized (acute or obtuse) angle.

What is the anglebetween the hand of a clock in ~ 2:30?


At 2:30 the minute hand(red) points to the 6 and also the hour hand(blue) points halfway between the 2 and the 3.

therefore how countless lots the 30° carry out we have actually this time?


The angle between the 5 and the 6 is30°The angle in between the 4 and also the5 is30°The angle in between the 3 and the4 is30°The continuing to be angle is½ × 30° = 15°

therefore the anglebetween the hands of a clock at2:30 = 30° + 30° + 30° + 15° = 105°

Your Turn

complete the adhering to table (give the smaller angle in each case):


Check her answers in ~ the bottom the the page.

More complex Times

Finding the angle between the hand of a clock is basic as longas us don"t use complex times.

For instance finding the anglebetween the hands at 9:37 is much an ext difficult. You have the right to trythat one if you wish, yet it"s probably too hard.

Example: Atwhat time is the angle in between the hand of a clock equal to30°?

an alert that the question asks for "times".There are many possibleanswers.Some of lock are simple to find, others much an ext difficult.

Here space two basic answers:

1 o"clock11 o"clock
But what aboutthis one?
4:15 PM

At first glance, the looks favor this might be a 30° edge also,but at 4:15, the hour hand has currently moveda 4 minutes 1 of the means between the 4 and also the 5.

So theangle is30°+ ¼ × 30° = 30° + 7½° = 37½°.

This might be a much more accurate answer:


have the right to you find more 30° angles choose this one?

At what times of the day do the hand of a clock lie in a straightline?

In various other words the angle in between them is 180°?

One obvious answer is 6 o"clock:


But what various other answers can there be?

9:15 is not correct for a similar reason the 4:15 didn"t provide us precisely a30° edge ... The hour hand has actually moved on past the 9.

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This seems to be a very difficult question to answer, yet there is aneasy way.

How many times in between 6:00 am and 6:00 pm do the hands do astraight line?

There have to be at the very least one allude time because that each hour:

one between 7:00 am and 8:00 am, one between 8:00 am and also 9:00 am, one between9:00 am and also 10:00 am, etc, approximately between 4:00 pm and 5:00 pm

That provides 11 equal parts, and also so: