Question

acute - angle
obtuse - angle
right - angle
straight - angle

Explanation:

Step1: Calculate angle per hour - mark

The clock face is 360°. There are 12 hour - marks. So the angle between each hour - mark is $\frac{360}{12}=30^{\circ}$.

Step2: Determine the positions of hands

The hour hand is between 11 and 12, and the minute hand is on 9. The hour hand moves 30° per hour and a fraction of that in 45 minutes (since the minute hand is at 9 which is 45 minutes past the hour). In 45 minutes, the hour hand moves $\frac{45}{60}\times30 = 22.5^{\circ}$ past the 11 - o'clock mark. The angle between 9 and 11 is $2\times30 = 60^{\circ}$, and adding the extra 22.5° that the hour hand has moved past 11, the angle between the hands is $60 + 22.5=82.5^{\circ}$.

Step3: Classify the angle

An acute angle is an angle less than 90°. Since $82.5^{\circ}<90^{\circ}$, it is an acute angle.

Answer:

Acute angle