What is the measure of the angle of the hands on a clock if it is 3:24?

from 3 o’clock until 3:20, the minute hand will move 1/3 of the way around the circle or 120 degrees. But the hour hand has also moved 1/3 of the way to the next number, or 10 degrees.

42deg

Step-by-step explanation:

Let's see.

We'll consider 12:00 the "starting position"

The minute hand moves with the speed of 360deg in an hour, so 6deg per minute.

The hour hand moves with the speed of 360deg in 12hours, so 30deg per hour, so 0.5deg per minute.

at 3:24, the minute hand has moved 24*6deg=144deg from the starting position, while the hour hand has moved by 3*30deg + 24*0.5deg = 102deg

The absolute difference of the angles is 144deg-102deg = 42deg and it's the angle between the hands.

C. 6  

Step-by-step explanation:

∆ABC and ∆ADE are similar triangles.

                       AB/AC = AD/AE

(x - 1 + x + 2)/(15 + 24) = (x - 1)/15

                 (2x + 1)/39 = (x - 1)/15         Multiply each side by 39

                        2x + 1 = 39(x - 1)/15     Multiply each side by 15

                   15(2x + 1) = 39(x - 1)         Distribute 15 and 39

                    30x + 15 = 39x - 39        Add 39 to each side

                   30x + 54 = 39x               Subtract 30x from each side

                              54 = 9x                Divide each side by 9

                                x = 6

Check:

(6 - 1 + 6 + 2)/(15 + 24) = (6 - 1)/15

                          13/39 = 5/15

                                ⅓ = ⅓