Find the angle measure

Question

The time shown on an analog clock is 8:10. What is the measure of the angle formed by the hands of the clock?

Answer 1

FINAL ANSWER: 175deg

I am going to take this in 2 steps to explain why.:

I.

If you make an assumption that the HOUR hand doesn't move from the 8 until the MINUTE hand reaches the 12 again, then at 8:10, the HOUR and MINUTE hands would form a straight line, or 180deg [6 numbers from 8 to 2 out of 12 numbers, so 6/12=1/2 the 360deg clock circle, and (1/2)(360deg)=180deg].

II.

HOWEVER: if the HOUR hand moves proportionally and evenly from number to number as the the MINUTE hand moves around the clock from 12 back to 12,.you have to adjust your result. When the MINUTE hand is on 2, the MINUTE hand has traveled 2/12=1/6 of the way around the 360deg clock circle, or (1/6)360deg=60deg. Proportionately, the HOUR hand also have to move 1/6 of the way from 8 to 9; and since 8 to 9 is 1/12 of the way around the 360deg clock circle, we have (1/12)360deg=30deg from 8 to 9, and 1/6 of that being how far the HOUR hand traveled, or

(1/6)(1/12)(360deg)=5deg.

Since the HOUR hand is 5deg closer to the MINUTE hand than, in step I. when we assumed the HOUR hand stayed on the 8 until the MINUTE hand hit 12 again, we have to subtract 5deg from our original 180deg

180-5=175deg.

FINAL ANSWER:

At 8:10, the hour and minute hand are 175deg apart.

Answer 2

the angle between the 2 hands is 2/12 of the circle. There are 360 degrees in a circle so the angle is (2/12)(360)= 60 degrees