Question

in circle o, rt and su are diameters. if mrv = mvu, what is mvu? 47° 52° 64° 87°

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. The angle opposite to the $13x^{\circ}$ and the angle opposite to $(15x - 8)^{\circ}$ are vertical angles. So, $13x=15x - 8$.

Step2: Solve the equation for $x$

Subtract $13x$ from both sides: $0 = 15x-13x - 8$, which simplifies to $0 = 2x - 8$. Then add 8 to both sides: $8 = 2x$. Divide both sides by 2, we get $x = 4$.

Step3: Find the measure of the central angle corresponding to arc $VU$

Substitute $x = 4$ into the expression for the central - angle of arc $VU$, which is $13x^{\circ}$. So the central angle of arc $VU$ is $13\times4^{\circ}=52^{\circ}$.

Step4: Recall the relationship between arc measure and central - angle measure

The measure of an arc is equal to the measure of its central angle. Since $m\overset{\frown}{RV}=m\overset{\frown}{VU}$, and we found the measure of the central angle corresponding to arc $VU$ is $52^{\circ}$, then $m\overset{\frown}{VU}=52^{\circ}$.

Answer:

$52^{\circ}$