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prealgebra intermediate

Problem

At

2 : 15

o'clock, the hour and minute hands of a clock form an angle of:

(A)

3 0^{\circ}

(B)

5^{\circ}

(C)

22 \frac{1}{2}^{\circ}

(D)

7 \frac{1}{2}^{\circ}

Solution

Using the formula

\frac{∣60 h - 11 m ∣}{2}

, where

h

is the hour time and

m

is the minute time, we get that the angle is

\frac{∣60 ( 2 ) - 11 ( 15 ) ∣}{2} = \frac{∣120 - 165∣}{2} = \frac{45}{2} = 22 \frac{1}{2}^{\circ}

Final answer

C