Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Ask your questions and receive precise answers from experienced professionals across different disciplines. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Circle theorem states that the angle that an arc subtends at the center of a
circle is twice the angle subtended at the circumference.
The values are as follows;
- m∠EDA = 90°
- m∠BDC = 21°
- m∠BEC = 21°
- [tex]m\widehat{AB}[/tex] = 80°
- m∠AEB = 40°
- m∠ECA = 29°
- m∠BAC = 21°
- [tex]m\widehat{ED}[/tex] = 90°
- m∠ECD = 45°
- m∠ACB = 40°
- m∠EBD = 45°
- m∠ADB = 40°
- m∠CAD = 45°
- m∠EAB = 90°
- m∠EBC = 90°
Reasons:
[tex]\displaystyle 1. \ \mathbf{m\angle EDA} = \frac{1}{2} \cdot m\angle EPC[/tex] Angle subtended at center is twice angle at circumference.
m∠EPC = 180°
∴ m∠EDA = 0.5 × 180° = 90°
2. [tex]m\widehat{BC}[/tex] = 42°, therefore, m∠BPC = 42°
[tex]\displaystyle \ m\angle BDC= \frac{1}{2} \cdot m\angle BPC[/tex]
m∠BDC = 0.5 × 42° = 21°
3. m∠BEC = m∠BDC = 21°
4. [tex]m\widehat{AB}[/tex] = 180° - (58° + 42°) = 80°
5. [tex]\mathbf{m\widehat{AB}}[/tex] = m∠APB by definition
m∠AEB = 0.5 × m∠APB
m∠AEB = 0.5 × 80° = 40°
6. m∠ECA = 0.5 × m∠AE
Therefore;
m∠ECA = 0.5 × [tex]m\widehat{EA}[/tex]
m∠ECA = 0.5 × 58° = 29°
m∠ECA = 29°
7. m∠BAC = 0.5 × [tex]\mathbf{m\widehat{BC}}[/tex]
m∠BAC = 0.5 × 42° = 21°
m∠BAC = 21°
8. [tex]m\widehat{ED}[/tex] = 180° - [tex]\mathbf{m\widehat{CD}}[/tex]
[tex]m\widehat{ED}[/tex] = 180° - 90° = 90°
[tex]\mathbf{m\widehat{ED}}[/tex] = 90°
9. m∠ECD = 0.5 × [tex]\mathbf{m\widehat{ED}}[/tex]
m∠ECD = 0.5 × 90° = 45°
10. m∠ACB = 0.5 × [tex]m\widehat{AB}[/tex]
m∠ACB = 0.5 × 80° = 40°
11. m∠EBD = 0.5 × [tex]\mathbf{m\widehat{ED}}[/tex]
m∠EBD = 0.5 × 90° = 45°
12. m∠ADB = 0.5 × [tex]\mathbf{m\widehat{AB}}[/tex]
m∠ADB = 0.5 × 80° = 40°
13. m∠CAD = 0.5 × [tex]\mathbf{m\widehat{CD}}[/tex]
m∠CAD = 0.5 × 90° = 45°
14. m∠EAB = 0.5 ×[tex]\mathbf{m\widehat{EABC}}[/tex]
m∠EAB = 0.5 × 180° = 90°
15. m∠EBC = 0.5 ×[tex]\mathbf{m\widehat{EABC}}[/tex]
m∠EBC = 0.5 × 180° = 90°
Learn more about circle theorems here:
https://brainly.com/question/25101481
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
