Question

question 3 of 10
which expression gives the measure of ∠xyz?
a. 110° - 42°
b. 1/2(110° + 42°)
c. 110° + 42°
d. 1/2(110° - 42°)

Explanation:

Step1: Recall the vertical angle theorem

The measure of an angle formed by two intersecting chords in a circle is half the sum of the measures of the intercepted arcs.

Step2: Identify the intercepted arcs

The intercepted arcs are \(110^{\circ}\) and \(42^{\circ}\).

Step3: Apply the formula

The formula for the measure of \(\angle XYZ\) is \(\frac{1}{2}(m\overset{\frown}{VW}+m\overset{\frown}{XZ})\). Substituting the values of the arcs \(m\overset{\frown}{VW} = 110^{\circ}\) and \(m\overset{\frown}{XZ}=42^{\circ}\), we get \(\frac{1}{2}(110^{\circ}+ 42^{\circ})\).

Answer:

B. \(\frac{1}{2}(110^{\circ}+42^{\circ})\)