Triangle $ABC$ is the image of triangle $DEC$, which is right-angled at $C$. We need to determine the angle of rotation around point $C$ that transforms triangle $DEC$ into triangle $ABC$.

1. Problem Description

Triangle $ABC$ is the image of triangle $DEC$, which is right-angled at $C$. We need to determine the angle of rotation around point $C$ that transforms triangle $DEC$ into triangle $ABC$.

2. Solution Steps

Observe the diagram. $C$ is the center of rotation.

The angle between $CE$ and $CA$ can be used to determine the angle of rotation. Also, note that the rotation is clockwise.

Since $\angle BCE$ appears to be a straight line and $C$ is the right angle, and the $\angle BCA$ is

1

8

0.

Visually, it appears that rotating $DEC$ by $90^\circ$ clockwise around $C$ would map $E$ to a point near $A$ and $D$ to a point near $B$.

Therefore, the angle of rotation is $-90^\circ$ (or $270^\circ$).

3. Final Answer

(b) $-90^\circ$