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mario62 [17]
3 years ago
13

Write an equation to represent the following statement. j is 7times as large as 6 .

Mathematics
1 answer:
Romashka-Z-Leto [24]3 years ago
3 0
6=j-7, sorry if it’s wrong
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In Circle P, m EA=58, m BC=42, m CD=90, find:
elena55 [62]

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;

  1. m∠EDA = <u>90°</u>
  2. m∠BDC = <u>21°</u>
  3. m∠BEC = <u>21°</u>
  4. m\widehat{AB} =<u> 80°</u>
  5. m∠AEB = <u>40°</u>
  6. m∠ECA =  <u>29°</u>
  7. m∠BAC = <u> 21°</u>
  8. <u />m\widehat{ED}  =  <u>90°</u>
  9. m∠ECD = <u>45°</u>
  10. m∠ACB = <u>40°</u>
  11. m∠EBD = <u>45°</u>
  12. m∠ADB = <u>40°</u>
  13. m∠CAD = <u>45°</u>
  14. m∠EAB = <u>90°</u>
  15. m∠EBC = <u>90°</u>

<u />

Reasons:

\displaystyle 1. \ \mathbf{m\angle EDA} = \frac{1}{2} \cdot m\angle EPC Angle subtended at center is twice angle at circumference.

m∠EPC = 180°

∴  m∠EDA = 0.5 × 180° = <u>90°</u>

2. m\widehat{BC} = 42°, therefore, m∠BPC = 42°

\displaystyle \ m\angle BDC= \frac{1}{2} \cdot m\angle BPC

m∠BDC = 0.5 × 42° =<u> 21°</u>

3. m∠BEC = m∠BDC = <u>21°</u>

4. m\widehat{AB} = 180° - (58° + 42°) =<u> 80°</u>

5. \mathbf{m\widehat{AB}} = 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\widehat{EA}

m∠ECA = 0.5 × 58° = 29°

m∠ECA =  <u>29°</u>

7. m∠BAC = 0.5 × \mathbf{m\widehat{BC}}

m∠BAC = 0.5 × 42° = 21°

m∠BAC = <u> 21°</u>

8. m\widehat{ED}  = 180° - \mathbf{m\widehat{CD}}

m\widehat{ED}  = 180° - 90° = 90°

\mathbf{m\widehat{ED}}  =  <u>90°</u>

9. m∠ECD = 0.5 × \mathbf{m\widehat{ED}}

m∠ECD = 0.5 × 90° = <u>45°</u>

10. m∠ACB = 0.5 × m\widehat{AB}

m∠ACB = 0.5 × 80° = <u>40°</u>

11. m∠EBD = 0.5 × \mathbf{m\widehat{ED}}

m∠EBD = 0.5 × 90° = <u>45°</u>

12. m∠ADB = 0.5 × \mathbf{m\widehat{AB}}

m∠ADB = 0.5 × 80° = <u>40°</u>

13. m∠CAD = 0.5 × \mathbf{m\widehat{CD}}

m∠CAD = 0.5 × 90° = <u>45°</u>

14. m∠EAB = 0.5 ×\mathbf{m\widehat{EABC}}

m∠EAB = 0.5 × 180° = <u>90°</u>

15. m∠EBC = 0.5 ×\mathbf{m\widehat{EABC}}

m∠EBC = 0.5 × 180° = <u>90°</u>

<u />

<u />

Learn more about circle theorems here:

brainly.com/question/25101481

3 0
3 years ago
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