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Hour hand covers an angle of 360 in 12 hours.
Time taken to cover an angle of 135 degree = (12 x 135)/360 =4.5 hr
Required time = 3 + 4.5 = 7.5 = 7:30

Hope this helps :)

The hour hand covers an angle of 360° in 12 hours

∴Time taken to cover an angle of 135° = 12/360 =4.5 h

∴ Required time = 3.00 + 4.5 = 7.5 = 7:30

Hence the time would be 7:30 after the hour hand moves 135° because it will cover 4½ hours in those 135° after 3:00.