Find the measures of the angle formed by the hands of a clock at 6:45

67.5°

Step-by-step explanation:

At 6:45, the minute hand is at 9

The hand is between 6 and 7

Angle between two digits on the clock: 360/12 = 30

Between 7 and minute hand:

2 * 30 = 60

Between hour hand and 7:

(60-45) / 60 * 30 = 7.5

Total:

60 + 7.5 = 67.5°

67.5 degrees

Step-by-step explanation:

The angle between the 6 and the 9 = 90 degrees.

WE can say that the hour hand is ' 3/4 of 5 minutes' past the 6.

5 minutes is equivalent to 360 / 12 = 30 degrees.

Thus the angle between the 6 and the hour hand

= 30 * 3/4

= 22.5 degrees.

The required angle is 90 - 22.5

= 67.5 degrees.