Question

wxyz is a rectangle. what is m∠yzx? (not drawn to scale) a 9 b 69 c 45 d 21

Explanation:

Step1: Use angle - sum property in right - triangle

In rectangle \(WXYZ\), \(\angle WZY = 90^{\circ}\), and \(\angle YZX+\angle WZV=90^{\circ}\). Also, since the diagonals of a rectangle are equal and bisect each other, \(\triangle WZV\) is isosceles, and \((x - 9)+(2x + 9)=90\).
\[

$$\begin{align*} x-9+2x + 9&=90\\ 3x&=90\\ x&=30 \end{align*}$$

\]

Step2: Find \(\angle YZX\)

Substitute \(x = 30\) into the expression for \(\angle YZX\) which is \(x-9\).
\(\angle YZX=x - 9=30-9 = 21^{\circ}\)

Answer:

D. 21