Question

question 2 of 10 if stuv is a rectangle and m∠vsu = 52°, what is the

Explanation:

Step1: Recall rectangle properties

In rectangle STUV, diagonals are equal and bisect each other, so $\triangle VSU$ is isosceles with $VS = SU$.

Step2: Find other base - angle

Since $\triangle VSU$ is isosceles and $\angle VSU=52^{\circ}$, the other base - angle $\angle SVU=\angle SUV$. Let $\angle SVU = \angle SUV = y$. Using the angle - sum property of a triangle ($\angle VSU+\angle SVU+\angle SUV = 180^{\circ}$), we have $52^{\circ}+2y = 180^{\circ}$, so $2y=180^{\circ}- 52^{\circ}=128^{\circ}$, and $y = 64^{\circ}$.

Step3: Identify the required angle

The angle marked as $x$ is $\angle SVU$, so $x = 64^{\circ}$.

Answer:

E. 64