Question

find the measure of the smaller angle formed by the hands of a clock at the following time. the angle is $square^{circ}$. (simplify your answer. type an integer or a simplified fraction.)

Explanation:

Step1: Know clock - face basics

A clock is a circle of 360°. The hour - hand moves 360° in 12 hours, so it moves 30° per hour ($\frac{360}{12}=30$). The minute - hand moves 360° in 60 minutes, so it moves 6° per minute ($\frac{360}{60}=6$).

Step2: Analyze the position of hands

At 11:00, the hour - hand is at 11 and the minute - hand is at 12. The hour - hand has moved $\frac{11}{12}$ of the way around the 12 - hour cycle.
The angle between each consecutive hour mark on the clock is 30°.
Since the minute - hand is at 12 and the hour - hand is at 11, the angle between the hands is 30°.

Answer:

30