[Math] What angle does minute hand and hour hand clock inclined to each other at $2:25$

Question

What angle does minute hand and hour hand clock inclined to each other at $2:25$

My Attempt:

The hour hand of a clock rotate throufh an angle of $30°$ in $1$ hour,

So,

At $2$o'clock, $2$ hrs$\equiv 60°$

Again,

The minute hand of a clock rotate through an angle of $6°$ in $1$ minute.

So, At $2:25$, i.e, $25$min$\equiv 150°$

What should I do further?

Answer 1

Time 2 hrs 25 minutes. Converting into hours $2\frac{25}{60} = 2 \frac5{12} = \frac {29}{12}$

Angle made by hour hand in $\frac {29}{12}$ hrs $= \frac{360}{12} \times \frac{29}{12} = \frac {145}{2} = 72.5°$

Angle made by minute hand in 25 min $= \frac{360}{60} \times 25 = 150°$

Difference in angle $= 150° - 72.5° = 77.5°$