Question

For the following figure, if $\overline{WR}\perp \overline{CE}$then name all angles congruent to $\angle RCE$.

Short answer

The angles are congruent to $\angle RCE$ is $\angle ECW,\angle WEC$ .

Step-by-step solution

Step 1. Check the figure.

Consider the figure $▱CREW$.

Step 2. Apply the concept of the parallelogram.

In a parallelogram, if the diagonals of a parallelogram are perpendicular then it is a rhombus.

In a rhombus, all sides are equal.

Step 3. Step description.

Here, $CREW$is a parallelogram.

Since $WR\perp CE$thus the parallelogram becomes a rhombus.

As all sides are equal in a rhombus thus the sides are as follows:

$\begin{array}{c}RC=CW\\ =WE\\ =RE\end{array}$

This triangle is an Isosceles triangle and in the Isosceles triangle, the base angle is equal then $\angle ECW=\angle WEC$.

Step 4. Step description.

From the figure, WE and CE is transversal thus alternate angles are equal such that $\angle RCE=\angle WEC$.

Therefore, the angles congruent to $\angle RCE$are $\angle ECW,\angle WEC$.