What is the measure of then angle formed by the minute hand and the hour hand at 8:24 PM?

Question

Thats it

Answer 1

1 minute tick at clock = 360 / 60 = 6 degree
At 24 minute, the angle from 0 minute is 6 x 24 = 144 degree.

At 8:00 PM the hour hand at 40 minute = 6 x 40 = 240 degree
At 8:24 PM the hour hand at 40 + (5 / 60 x 24) = 42 minute
= 6 x 42 = 252 degree

Angle between the two hands at 8:24 PM = 252 - 144 = 108 degree

Answer 2

At 8:24 pm

Minute hand is 24/60 = 2/5 of the way around the clock from 12:00 pm. In degrees that is:

(2/5)*360 = 144°

The hour hand:

8/12 + (1/12)(2/5) = 2/3 + 1/30 = 21/30 = 7/10

(7/10)*360 = 252°

The minute and hour hand form an angle of:

252 - 144 = 108°

Answer 3

Consider the 12 on the clock face to be 0°.

24 minutes is at 24/60 * 360° = 144°
The minute had is at 144°

The 8 is at 8/12 * 360° = 240°
The 9 is at 9/12 * 360° = 270°

At 8:24, the hour hand will be at 240 + (24/60)*(270-240) = 252°.

The angle between the minute hand and the hour hand is 252° - 144° = 108°

Answer 4

At 8:24, the hour hand has long previous 2/5 the way between the 8 and the 9, at the same time as the minute hand is 4/5 the way between 4 and 5. the attitude formed includes 3 3/5 cases the gap between 2 numbers (one million/5 to 5, 3 to eight, and a pair of/5 to the different hand). each and each extensive form is 360/12=30 tiers. consequently the attitude is 30 x (3 3/5), or 108 tiers. For those fellow math geeks obtainable who like reflex angles, 252 tiers is yet another answer.

Answer 5

Mmmm...

From 8h to 12hs, 1/3 turn

From 0 to 24min, 24/60 of turn

but the hour hand has gone 24/(60*12) of turn further than the 8.

Then, the angle is

360 * (1/3 + 24/60 - 24/(60*12)= 360*21/30= 252 degrees

Answer 6

hour= 240 degree
min =144 degree

Answer 7

45

Answer 8

238.8 degrees