Find each measure in OP if mZWPX = 28°, mZZPY = 38°, and WZ and XV are diameters. 1. YZ 5. ZXPY W 2. WX 6. XY V 3. ZVPZ 7. XWY 4. VWX 8. WZX Z Y
Answer (1)
Given:m∠ZWPX = 28°m∠ZYPY = 38°WZ and XV are diameters (implying ∠WZX = 90° and ∠XVW = 90°)Find each measure:1. YZ = 90° - 38° = 52° (since ∠ZYPY + ∠YZX = 90°)2. WX = 28° + 52° = 80° (since ∠ZWPX + ∠YZX = ∠WXZ)3. ZVPZ = 38° (vertical angles)4. VWX = 90° (since XV is a diameter)5. ZXPY = 28° (given)6. XY = 90° - 28° = 62° (since ∠WXZ + ∠ZXY = 90°)7. XWY = 62° (since ∠XWY = ∠ZXY)8. WZX = 90° (since WZ is a diameter)Note: These calculations assume a circle with center Z, and diameters WZ and XV intersecting at Z.[tex].[/tex]
