Question

in circle o, rt and su are diameters. if mrv = mvu, what is mvu? (13x)° (15x - 8)°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. 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: $2x=8$, and divide by 2 to get $x = 4$.

Step3: Find the measure of $\angle VOU$

Since $m\overset{\frown}{RV}=m\overset{\frown}{VU}$, and the measure of an arc is equal to the measure of its central - angle. The central angle corresponding to $\overset{\frown}{RV}$ is $13x$. Substitute $x = 4$ into $13x$, we get $13\times4=52^{\circ}$. So $m\overset{\frown}{VU}=52^{\circ}$.

Answer:

$52^{\circ}$