Question

stuv ~ wzyx. what is ( mangle v )? ( mangle v = square^circ )

Explanation:

Step1: Recall quadrilateral angle sum

The sum of interior angles of a quadrilateral is $360^\circ$.

Step2: Identify corresponding angles

Since $STUV \sim WZYX$, $\angle S \cong \angle W$, $\angle T \cong \angle Z$, $\angle U \cong \angle Y$, $\angle V \cong \angle X$.

Step3: Find unknown angle in WZYX

Let $m\angle W = a$, $m\angle Y = b$.
$a + 84^\circ + b + 125^\circ = 360^\circ$
$a + b = 360^\circ - 84^\circ - 125^\circ = 151^\circ$

Step4: Calculate $m\angle V$

In $STUV$, $a + 75^\circ + b + m\angle V = 360^\circ$
Substitute $a + b = 151^\circ$:
$151^\circ + 75^\circ + m\angle V = 360^\circ$
$m\angle V = 360^\circ - 151^\circ - 75^\circ = 66^\circ$

Answer:

$66^\circ$