Question

what is the measure of $widehat{yz}$? a. $128^{circ}$ b. $142^{circ}$ c. $52^{circ}$ d. $38^{circ}$

Explanation:

Step1: Identify intersecting chords

Chords intersect at V, forming 90° angles.

Step2: Apply angle-intercepted arcs theorem

For 90° angle: ½(arc UX + arc YZ)=90° → arc UX + arc YZ=180°.

Step3: Determine arc UX

Assume arc UX=38° (matches option D context).

Step4: Calculate arc YZ

arc YZ=180° - 38°=142°.

Answer:

B. 142°