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anonymous

  • one year ago

I can't find the missing angles.

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  1. anonymous
    • one year ago
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    |dw:1437537537663:dw|

  2. anonymous
    • one year ago
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    It is 60 and 60

  3. anonymous
    • one year ago
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    My textbook says that angle ABC=111 and angle CDE=129

  4. anonymous
    • one year ago
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    That is the answer but how do i get it?

  5. mathstudent55
    • one year ago
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    ABCDE is a pentagon.

  6. mathstudent55
    • one year ago
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    A pentagon has 5 sides. The sum of the measures of the internal angles of a pentagon is (n - 2)180 = (5 - 2)180 = 3(180) = 540

  7. mathstudent55
    • one year ago
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    |dw:1437538174022:dw|

  8. anonymous
    • one year ago
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    then the ? on the left is 51 and the ? on the right is 69

  9. anonymous
    • one year ago
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    math student 55 am i right?

  10. mathstudent55
    • one year ago
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    540 - 120 - 60 - 60 - 30 - 30 - 60 - 60 = 120 The sum of the measures of the missing angles is 120.

  11. anonymous
    • one year ago
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    I don't understand how you would get ? though.

  12. mathstudent55
    • one year ago
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    |dw:1437538419243:dw|

  13. mathstudent55
    • one year ago
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    |dw:1437538472592:dw|

  14. mathstudent55
    • one year ago
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    |dw:1437538502849:dw|

  15. anonymous
    • one year ago
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    How did you get 69?

  16. mathstudent55
    • one year ago
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    The inscribed angle <CDA is half the measure of the arc CBA

  17. anonymous
    • one year ago
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    i see

  18. mathstudent55
    • one year ago
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    |dw:1437538600159:dw|

  19. mathstudent55
    • one year ago
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    |dw:1437538634138:dw|

  20. anonymous
    • one year ago
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    Okay then. I see how you got it. Thanks for the help. :)

  21. mathstudent55
    • one year ago
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    I assumed that O is the center of the circle. Is my assumption correct?

  22. anonymous
    • one year ago
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    Yeah it is

  23. mathstudent55
    • one year ago
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    ok

  24. mathstudent55
    • one year ago
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    Then you don't need to use the angles of a pentagon like I did above.

  25. mathstudent55
    • one year ago
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    You need to know that a central angle measures the same as its arc. An inscribed angle measures half of its arc.

  26. mathstudent55
    • one year ago
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    |dw:1437538880449:dw|

  27. anonymous
    • one year ago
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    Oh i was kinda confused about why the inscribed measures half of its arc.

  28. mathstudent55
    • one year ago
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    Here is how you solve this problem. It is very few steps. 1. Arcs DE and BA are 60 degrees like their central angles. |dw:1437538961885:dw|

  29. mathstudent55
    • one year ago
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    2. Arc CDE is 42 + 60 = 102 deg m<CBE = 51 |dw:1437539067048:dw|

  30. mathstudent55
    • one year ago
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    3, Subtract 360 - 42 - 60 - 120 - 60 = 78 to find arc BC If BC = 78, then arc ABC = 138 m<CDA = 1/2 m(arc)ABC = 69 |dw:1437539126457:dw|

  31. mathstudent55
    • one year ago
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    That's it.

  32. anonymous
    • one year ago
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    Thanks @mathstudent55 :D Your the best! I understand it better now.

  33. mathstudent55
    • one year ago
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    You're welcome.

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