The angle between the hour hand and the minute hand of a clock at the time 9.38 pm is

Minute hand comples $$360\degree$$ in $$60$$ minutes. 

This means in a minute it covers $$\dfrac{360}{60} = 6\degree$$

The minute hand at $$38$$ minutes is at $$38 \times 6\degree = 228\degree$$ from the $$12$$ mark. 

The hour hand covers $$360\degree$$ in $$12$$ hours. In one hour it covers $$ \dfrac{360}{12} = 30\degree$$. And in one minute it covers $$\dfrac{30\degree}{60} = 0.5\degree$$

Thus, the hour hand is at $$9 \times 30\degree + 38 \times 0.5\degree = 270\degree + 19\degree = 289\degree$$. 

The angle between them is $$289\degree - 228\degree = 61\degree$$.