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Example: Finding Angle Measure

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Clock angle problem


Clock angle problems are a type of mathematical problem which involve finding the angles between the hands of an analog clock. Questions of this nature may appear in text books, tests, examinations or mathematics competitions.



The diagram shows the angles formed by the hands of an analog clock showing a time of 2:20


Math problem

Clock angle problems relate two different measurements: angles and time. To answer the problem the relationship between the time shown (or an elapsed time) and the position of the hands (as given by an angle) has to be found.

A general approach to such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute. The minute hand rotates through 360° in 60 minutes or 6° per minute. (Our solved example in mathguru.com uses this concept)

Equation for the degrees on the minute hand

θmin. = 6M


1.  is the angle in degrees of the hand measured clockwise from the 12 o'clock position.

2. M is the minute

(Our solved example in mathguru.com uses this concept)




The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.