Question

1. there is a square, abcs, inscribed in a circle with center d. what is the smallest angle we can rotate around d so that the image of a is b? draw a picture if it helps you! 45° 60° 90° 180°

Explanation:

Step1: Recall the properties of a square inscribed in a circle

When a square is inscribed in a circle, the central angles between consecutive vertices are equal. The total central angle around a point is \(360^{\circ}\).

Step2: Calculate the central angle between two consecutive vertices of the square

Since a square has \(4\) equal - length sides, the measure of the central angle \(\theta\) between two consecutive vertices (e.g., from \(A\) to \(B\)) is given by the formula \(\theta=\frac{360^{\circ}}{n}\), where \(n = 4\) (the number of sides of the square).

$$ \theta=\frac{360^{\circ}}{4}=90^{\circ} $$

Answer:

\(90^{\circ}\) (the third option)