Question

practice 4 (from unit 1, lesson 14)
there is a square, abcd, inscribed in a circle with center o. what is the smallest angle we can rotate around o so that the image of a is b?
a 45°
b 60°
c 90°
d 180°

Explanation:

Step1: Recall properties of a square inscribed in a circle

The central angles subtended by the sides of a square inscribed in a circle are equal. The sum of central - angles around a point is 360°. Since a square has 4 equal - length sides, the central angle between two adjacent vertices (e.g., from A to B) is $\frac{360^{\circ}}{4}$.

Step2: Calculate the central angle

$\frac{360^{\circ}}{4}=90^{\circ}$. The smallest angle of rotation around the center O of the circle to map point A to point B is equal to the central angle subtended by side AB at the center O of the circle.

Answer:

C. 90°