What is the degree measure of the angle formed by the hands of an analog clock at 7:48? At 1:20? Explain how?

Question

First explain what the problem is stating and asking, then make a plan of what you are to do, then solve, then explain how and why

Answer 1

Things to remember...

360 Degrees in a circle
180 Degrees in half circle
30 Degrees per every hour marker on the clock
6 Degrees per every minute maker on the clock

When the hour hand is at 7 then your starting angle is 210 Degrees.
When the minute hand is at 48 then your ending angle is 288.
The difference in these angles is 78 Degrees which is your answer for the first problem.

When the hour hand is at 1 then your starting angle is 30 Degrees.
When the minute hand is at 20 then your ending angle is 120.
The difference in these angles is 90 Degrees which is your answer for the second problem.

Answer 2

You are asked to determine the angle between the minut hand and the hour hand at 7:48. So we must find the angular difference between and the hour hand.

The minute hand will have traveled 48/60 of 360 degrees since 7:00 o'clock or 288 degrees.

the angle between 7 and 8 o,clock is 30 degrees and the hour hand will have traveked 48/60 of 30 degrees = 24 degrees
So the hour is now at 7*30+24 = 234 degrees .

The difference is 288 - 234 = 54 degrees

At 1:20 the minute hand is pointing at 4 so has traveled 120 degrees or 1/3 of the way around the clock since 1 o'clock.
During this same time the hour hand has ta=ravled 1/3 of the way between 1 and 2 o'clock so is now pointing at 30 +1/3 of 30 = 40 degrees. Hence the angle between the two hands is
120- 40 = 80 degrees.

Answer 3

the hour hand takes 12 hours to cover360 degrees
the minute hand takes 60 minutes to cover 360 degrees

at 7.48
the angle formed by the hour hand=7 48/60/12*360 degrees
=39*360/12*5 degrees=234 degrees.

the angle formed by the minute hand=48/60 *360=268 degrees
so the angle between the hands=34 degrees

at 1.20
the angle formed by the hour hand=1 1/3/12*360=4*360/12*3=40 degrees

the angle formed by the minute hand=20/60*360degrees
=120 degrees
so the angle between the hands=80 degrees

Answer 4

There are 60 minute-marks on a clock and the difernce between two such marks is 6 degrees(360/60)
Again The hour hand moves one minute-mark in every (60/5 or 12 minutes
At 7-48 hrs,the hour hand would be 4 minute-mark away from 7 & the minute-hand would be 3 minute-marks away from 9.Hence ther would be differene of 9 minute-marks between them.Therefore,the angle would be 9X6=54 degrees
At 1-20,the hour-hand would be at(20/12)=1.66 minute-marks away from 1,whereas the minute-hand would be at 4 which is 15 marks away from 1.Therefore,there would be a difference(15-1.66) or 13.33 marks.
Therefore the angle between the two hands is 13.33X6=80 degrees

Answer 5

Good question,
There are many ways of looking at this, so here is my way.
If there is 360 degrees in a circle, 60 min in an hour, then there is 6 degrees in every min.
I added all the min and came up with 332 min, divided by 6 = 55.3 degrees between the time stated in the question.

Answer 6

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