All about plane geometry....?

Question

The question goes like this: Form two times when the hands of a clock form a straight angle...

I just want to be completely sure...

Answer 1

Straight angle is 180 degrees, so it's at 6 o'clock and (roughly, as the hour hand moves) 9:15.

Answer 2

Find two different times when the hands of a clock form a straight angle.

The obvious answer is 6 o'clock. Now let's find the next time.

Let
12 = distance once around the clock
r = rate at which hour hand travels
12r = rate at which minute hand travels
d = distance hour hand travels until next straight angle
d + 12 = distance minute hand travels until next straight angle

time = distance/rate

time = d/r = (d + 12)/(12r)
12dr = r(d + 12)
12dr = dr + 12r
11dr = 12r
11d = 12
d = 12/11

The time for the hour hand to travel distance 12/11 is
12/11 hours.

So every 12/11 hours the hands of the clock form a straight angle. The times for this to happen are:

6 = 6:00:00
7 1/11 ≈ 7:05:27
8 2/11 ≈ 8:10:55
9 3/11 ≈ 9:16:22
etc.

Answer 3

6:00 am and 6:00 pm
theres no other angle because the hour hand moves 6 degrees every minute.