Angles - clock hands

Find the angle that the large hand makes with the small hand of the clock - the central angle at 12:30. Find the magnitude of the smaller angle (if possible).
(Help: it's enough if you calculate how big an angle the hands make if they are 1 minute apart. A circle has 360°, and an hour has 60 minutes)

Correct answer:

A =  165 °

Step-by-step explanation:

$$\begin{gathered} m=\frac{30}{60}=\frac{1}{2}=0.5 \\ h=\frac{m}{12}=\frac{0.5}{12}=\frac{1}{24}\doteq 0.0417 \\ a=m-h=0.5-0.0417=\frac{11}{24}\doteq 0.4583 \\ A=360\cdot a=360\cdot 0.4583=165^{\circ } \end{gathered}$$

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