How would I go about finding the possibilitys

Question

At some time between 9:30 and 10 o'clock the triangle determined by the minute hand and the hour hand of the clock is a isosceles triangle. If two equal angles in this triangle are each twice as large as the third angle, and the hands are of different lengths, determine all possible times.

Answer 1

Look at a clock!

At 9:30 the angle is 105°

Every minute the minute hand moves 6° and the hour hand moves 0.5°

How many minutes pass before the angle contracts to 36°? (5x = 180)

92.5 - 6m + 0.5m = 36

92.5 - 5.5m = 36

92.5 = 36 + 5.5m

56.5 = 5.5m

10.27 = m

 

Answer 2

I was working on this problem, too and Mark M. solved it beautifully!