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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 = <u>90°</u>
- m∠BDC = <u>21°</u>
- m∠BEC = <u>21°</u>
=<u> 80°</u>
- m∠AEB = <u>40°</u>
- m∠ECA = <u>29°</u>
- m∠BAC = <u> 21°</u>
- <u />
= <u>90°</u>
- m∠ECD = <u>45°</u>
- m∠ACB = <u>40°</u>
- m∠EBD = <u>45°</u>
- m∠ADB = <u>40°</u>
- m∠CAD = <u>45°</u>
- m∠EAB = <u>90°</u>
- m∠EBC = <u>90°</u>
<u />
Reasons:
Angle subtended at center is twice angle at circumference.
m∠EPC = 180°
∴ m∠EDA = 0.5 × 180° = <u>90°</u>
2. = 42°, therefore, m∠BPC = 42°
m∠BDC = 0.5 × 42° =<u> 21°</u>
3. m∠BEC = m∠BDC = <u>21°</u>
4. = 180° - (58° + 42°) =<u> 80°</u>
5. = m∠APB by definition
m∠AEB = 0.5 × m∠APB
m∠AEB = 0.5 × 80° = <u>40°</u>
6. m∠ECA = 0.5 × m∠AE
Therefore;
m∠ECA = 0.5 ×
m∠ECA = 0.5 × 58° = 29°
m∠ECA = <u>29°</u>
7. m∠BAC = 0.5 ×
m∠BAC = 0.5 × 42° = 21°
m∠BAC = <u> 21°</u>
8. = 180° -
= 180° - 90° = 90°
= <u>90°</u>
9. m∠ECD = 0.5 ×
m∠ECD = 0.5 × 90° = <u>45°</u>
10. m∠ACB = 0.5 ×
m∠ACB = 0.5 × 80° = <u>40°</u>
11. m∠EBD = 0.5 ×
m∠EBD = 0.5 × 90° = <u>45°</u>
12. m∠ADB = 0.5 ×
m∠ADB = 0.5 × 80° = <u>40°</u>
13. m∠CAD = 0.5 ×
m∠CAD = 0.5 × 90° = <u>45°</u>
14. m∠EAB = 0.5 ×
m∠EAB = 0.5 × 180° = <u>90°</u>
15. m∠EBC = 0.5 ×
m∠EBC = 0.5 × 180° = <u>90°</u>
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Learn more about circle theorems here: