Question

what is the measure of arc yz if the measure of angle wvx is 56.3 degrees and the measure of arc wx is 20.7 degrees?
91.9°
133.3°
35.6°
77.0°

Explanation:

Step1: Recall the vertical angles theorem

The measure of an angle formed by two intersecting chords is half the sum of the measures of the intercepted arcs. So, \(m\angle WVX=\frac{1}{2}(m\overset{\frown}{WX}+m\overset{\frown}{YZ})\).

Step2: Substitute the known values

Given \(m\angle WVX = 56.3^{\circ}\) and \(m\overset{\frown}{WX}=20.7^{\circ}\). Substitute into the formula: \(56.3=\frac{1}{2}(20.7 + m\overset{\frown}{YZ})\).

Step3: Solve for \(m\overset{\frown}{YZ}\)

Multiply both sides by 2: \(56.3\times2=20.7 + m\overset{\frown}{YZ}\). So, \(112.6=20.7 + m\overset{\frown}{YZ}\). Then subtract 20.7 from both sides: \(m\overset{\frown}{YZ}=112.6 - 20.7\).

Answer:

\(91.9^{\circ}\)