Question

wxyz is a rectangle. what is m∠yzx? (not drawn to scale) a 13 b 53 c 37 d 23

Explanation:

Step1: Use property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So, $\triangle WZV$ is isosceles and $\angle WZV=\angle XYZ$. Also, $\angle YZX+\angle WZX = 90^{\circ}$. And since $\angle WZX=(4x - 7)^{\circ}$ and $\angle YZX=(5x - 2)^{\circ}$, we know that $(4x - 7)+(5x - 2)=90$.

Step2: Solve the equation for x

Combine like - terms: $4x+5x-7 - 2=90$, which simplifies to $9x-9 = 90$. Add 9 to both sides: $9x=90 + 9=99$. Divide both sides by 9: $x=\frac{99}{9}=11$.

Step3: Find the measure of $\angle YZX$

Substitute $x = 11$ into the expression for $\angle YZX$. $\angle YZX=(5x - 2)^{\circ}=(5\times11 - 2)^{\circ}=(55 - 2)^{\circ}=53^{\circ}$.

Answer:

B. 53