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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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### Directions: Find each angle and arc measures.

**Problem 1.**
- **Figure Description:** A circle with chord WX and chord ZY intersecting at point V inside the circle. The angle WVZ is given as 62°.
- **Question:** \( m\angle WXY = \_\_\_\_\_\_ \)

**Problem 2.**
- **Figure Description:** A circle with points D, G, F, and E on the circumference. Arc DEF is highlighted, and angle DEG is given as 113°.
- **Question:** \( mDG\!F = \_\_\_\_\_\_ \)

**Problem 3.**
- **Figure Description:** A circle with chord PQ intersecting chord QR at point P inside the circle. Angle PQR is required to be measured, and arc QR is labeled with measure S.
- **Question:** \( m\angle PQR = \_\_\_\_\_\_ \)

**Problem 4.**
- **Figure Description:** A circle with points A, B, C, and D on the circumference. Arc AC is labeled and needs to be measured. Angle AB is given as 47°.
- **Question:** \( mBC = \_\_\_\_\_\_ \)

**Problem 5.**
- **Figure Description:** A circle with points J, K, L, and M on the circumference. Chord JK and segment ML intersect at point N within the circle. Angle KNM is given as 53° and angle JML (exterior) is labeled as 65°.
- **Question:** \( m\angle JKL = \_\_\_\_\_\_ \)

**Problem 6.**
- **Figure Description:** A circle with labeled points R, S, T, U. Arcs between these points are labeled with measures. Arcs RS equals 64°, ST equals 75°, and TU equals 139°.
- **Questions:**
  - \( m\angle RST = \_\_\_\_\_\_ \)
  - \( m\angle RUT = \_\_\_\_\_\_ \)

### Detailed Explanation of Diagrams:

**1.**
- Figure shows intersecting chords which creates vertical angles. The angle given is outside the area, which is 62°.

**2.**
- The major arc DEF is clear with 113° represented as the measurement of angle DEG.

**3
Transcribed Image Text:### Directions: Find each angle and arc measures. **Problem 1.** - **Figure Description:** A circle with chord WX and chord ZY intersecting at point V inside the circle. The angle WVZ is given as 62°. - **Question:** \( m\angle WXY = \_\_\_\_\_\_ \) **Problem 2.** - **Figure Description:** A circle with points D, G, F, and E on the circumference. Arc DEF is highlighted, and angle DEG is given as 113°. - **Question:** \( mDG\!F = \_\_\_\_\_\_ \) **Problem 3.** - **Figure Description:** A circle with chord PQ intersecting chord QR at point P inside the circle. Angle PQR is required to be measured, and arc QR is labeled with measure S. - **Question:** \( m\angle PQR = \_\_\_\_\_\_ \) **Problem 4.** - **Figure Description:** A circle with points A, B, C, and D on the circumference. Arc AC is labeled and needs to be measured. Angle AB is given as 47°. - **Question:** \( mBC = \_\_\_\_\_\_ \) **Problem 5.** - **Figure Description:** A circle with points J, K, L, and M on the circumference. Chord JK and segment ML intersect at point N within the circle. Angle KNM is given as 53° and angle JML (exterior) is labeled as 65°. - **Question:** \( m\angle JKL = \_\_\_\_\_\_ \) **Problem 6.** - **Figure Description:** A circle with labeled points R, S, T, U. Arcs between these points are labeled with measures. Arcs RS equals 64°, ST equals 75°, and TU equals 139°. - **Questions:** - \( m\angle RST = \_\_\_\_\_\_ \) - \( m\angle RUT = \_\_\_\_\_\_ \) ### Detailed Explanation of Diagrams: **1.** - Figure shows intersecting chords which creates vertical angles. The angle given is outside the area, which is 62°. **2.** - The major arc DEF is clear with 113° represented as the measurement of angle DEG. **3
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