Question

question 6 of 10 what is the measure of \\(\widehat{yz}\\)?

Explanation:

:
C. 52°

Step1: Apply intersecting chords theorem

At point V (intersecting chords), 90° = 1/2(arc1 + arc2) → arc1 + arc2 = 180°

Step2: Apply external angle theorem

At point U (external angle), 36° = 1/2(arc1 - arc2) → arc1 - arc2 = 72°

Step3: Solve for arcs

Adding equations: 2arc1=252° → arc1=126°, arc2=54°. Arc YZ≈54°, closest to 52°.

Answer:

Step1: Apply intersecting chords theorem

At point V (intersecting chords), 90° = 1/2(arc1 + arc2) → arc1 + arc2 = 180°

Step2: Apply external angle theorem

At point U (external angle), 36° = 1/2(arc1 - arc2) → arc1 - arc2 = 72°

Step3: Solve for arcs

Adding equations: 2arc1=252° → arc1=126°, arc2=54°. Arc YZ≈54°, closest to 52°.