Question

At what time between 9 and 10 will the hands of a watch makes an angle of 45/2

(1) 10 minutes past 9
(3) 25 minutes past 9
(2) 15 minutes past 9
(4) 45 minutes past 9​

Answer 1

Answer:

Step-by-step explanation:

At 9:x the minute hand is at x and it makes an angle = 6x deg from 12,

At 9:x the hour hand is between 9 and 10 and it makes an angle = 9*30 +x*30/60 = 270+0.5x deg from 12,

At 9:x the hour and the minute hands make an angle = 270+0.5x - 6x which is 45/2 = 22.5 deg, or

270–5,5x = 22,5, or

270–22.5 = 247.5 = 5.5x, or

x = 247.5/5.5 = 45

So at 9:45 the two hands of the clock make an angle = 22.5 deg between them.

Check: At 9.45, the minute hand is at 9 and it makes 9*30 = 270 deg from 12.

At 9.45, the hour hand is between 9 and 10 and it makes =9*30+45*30/60 = 270 +22.5 = 292.5 deg from 12.

At 9.45, the minute and the hour hands makes an angle = 292.5–270 = 22.5 deg. Correct.

Answer 2

Answer:

(4) 45 minutes past 9. is the correct answer