Question

in the diagram of circle c, ( mangle vwx ) is ( 43^{circ} ). what is ( mwidehat{vx} )?

Explanation:

Step1: Recall the formula for the measure of an angle formed by two secants

The measure of an angle formed by two secants outside a circle is $\frac{1}{2}(m\overset{\frown}{UY}-m\overset{\frown}{VX})$.

Step2: Substitute the known values

We know that $m\angle VWX = 43^{\circ}$ and $m\overset{\frown}{UY}=125^{\circ}$. So, $43^{\circ}=\frac{1}{2}(125^{\circ}-m\overset{\frown}{VX})$.

Step3: Solve the equation

Multiply both sides by 2: $43^{\circ}\times2 = 125^{\circ}-m\overset{\frown}{VX}$, which gives $86^{\circ}=125^{\circ}-m\overset{\frown}{VX}$. Then, $m\overset{\frown}{VX}=125^{\circ}- 86^{\circ}$.

Answer:

$39^{\circ}$