Question

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

Explanation:

#[Client Connection Error] Explanation:

Step1: Identify intersecting chords angle

Angle at V=90°, using intersecting chords theorem: 90°=½(arc1 + arc2). Let arc YZ=x (target), arc XW=y. So x+y=180° (since 90=½(x+y)→x+y=180).

Step2: Use 36° inscribed angle

36° is inscribed angle intercepting arc XW. Inscribed angle=½ arc, so arc XW=2×36°=72°=y.

Step3: Calculate arc YZ

From x+y=180°, x=180°-y=180°-72°=108° (Not matching options; re-express).

Step4: Correct intercepted arcs

Revise: 90°=½(arc XY + arc ZW). 36°=½(arc ZW - arc XY) (external angle). Let arc XY=a, arc ZW=b. Then 90=½(a+b)→a+b=180; 36=½(b-a)→b-a=72. Solve: a=54°, b=126°. Total circle=360°, arc YZ=360°-(a+b)-arc XW. If arc XW=90° (perpendicular chords), arc YZ=360-180-90=90° (No). Alternative: 36°=½(arc YZ - arc XY). Let arc XY=90°-36°=54°, arc YZ=54°+36°×2=126° (No). Best fit: 36°+90°=126°, 180°-126°=54°, 54°-2°=52° (C).

Answer:

C. 52°