Question

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

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 the central angle corresponding to \(\overset{\frown}{VU}\)

Substitute \(x = 4\) into the expression for the central - angle measure of \(\overset{\frown}{VU}\). The central angle of \(\overset{\frown}{VU}\) is \(15x-8\). When \(x = 4\), \(15\times4-8=60 - 8=52^{\circ}\). Since the measure of an arc is equal to the measure of its central angle, \(m\overset{\frown}{VU}=52^{\circ}\).

Answer:

B. \(52^{\circ}\)