Angles

leonswati wrote:What is the measure of the acute angle formed by the hands of a clock at 4:20 a.m.?


The answer is 10 deg.... Can someone explain it how?

Hi!

You'd definitely benefit from drawing out a clock on this question (as you would on pretty much any geometry question). Sadly, computer-generating diagrams is not one of my strengths, so we'll just visualize.

Let's think about where the hands are at 4:20: the little hand is on the 4 (20 minutes after the hour) and the big hand is somewhere between the 4 and the 5 (since it's between 4 and 5 pm). If you had provided answer choices (please always provide choices in the future, since a LOT of GMAT strategies involve working the answers), we may already have enough info to answer, since:

360 degrees/12 hours = 30 degrees per hour

and if we know that the two hands are both between 4 and 5, we know the answer must be less than 30.

If there's more than one answer under 30, then we'd go one step further. 20 minutes is 1/3 of an hour, so the big hand will be 1/3 of the way between the 4 and the 5. Since one hour is 30 degrees, 1/3 of an hour is 10 degrees.

Therefore, with the little hand right on the 4 and the big hand 10 degrees away from the 4, the two hands are 10 degrees apart!

Let 12'o clock be the reference.

Angle moved by the minute hand at 4:20 = 120 deg

What is the angle between 4'o clock and 5'o clock?
it is (1/12)th of 360 = 30 deg

At 20 minutes past 4, how much angle of this 30 deg will the minute hand cover?
(1/3)rd of it because 20 minutes is (1/3)rd of an hour.

So,
Angle moved by the hour hand at 4:20 = 120 + 1/3rd of 30 deg
= 120 + 10 deg

So, the angle between them = (120 + 10) - 120 = 10 deg