If STUV is a rectangle and the measure of angle VSU is 52 degrees, what is the valu...
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Problem
If STUV is a rectangle and the measure of angle VSU is 52 degrees, what is the value of x?
Step-by-step solution
In a rectangle, the diagonals bisect each other and are equal in length. Triangle VSU is a right-angled triangle, so $\angle SVU + \angle VSU = 90^{\circ}$. Given $\angle VSU = 52^{\circ}$, we have $\angle SVU = 90^{\circ} - 52^{\circ} = 38^{\circ}$. Since the diagonals of a rectangle bisect each other, the angle $x$ is equal to $\angle SVU$. Therefore, $x = 38^{\circ}$.
Answer
$38^{\circ}$