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anonymous

  • one year ago

The measure of arc AXB is 196. What is the measure of the tangent-chord angle ABC? http://media.apexlearning.com/Images/200701/18/55e3ff85-2144-4d69-9c27-2b7789a8d76c.gif

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  1. anonymous
    • one year ago
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    i reaalllyyyyy need the help :) please

  2. welshfella
    • one year ago
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    the m<ABC will be equal to the measure of the angle subtended by the chord in the opposite segment

  3. welshfella
    • one year ago
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    |dw:1434905469876:dw|

  4. welshfella
    • one year ago
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    you can use the fact that the arc AXB = 196 degrees to find the value of this angle

  5. anonymous
    • one year ago
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    is there a formula i can plug this into?

  6. welshfella
    • one year ago
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    I never did arcs when in college (many years ago) so i'm not sure!. Sorry you'll have to google that - or someone else probably knows

  7. welshfella
    • one year ago
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    there's probably a theorem

  8. welshfella
    • one year ago
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    |dw:1434906010781:dw|

  9. welshfella
    • one year ago
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    the angle marked is 360 - 196 = 164 degrees

  10. welshfella
    • one year ago
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    this is the angle at the center of the circle

  11. anonymous
    • one year ago
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    then do you subtract it from 180 and with that answer divide by 2?

  12. welshfella
    • one year ago
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    |dw:1434906331031:dw|

  13. welshfella
    • one year ago
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    that angle is 82 because its 1/2 of 164

  14. welshfella
    • one year ago
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    now opposite angles of a cyclic quadrilateral add up to 180 so the opposite angle = 180 - 82 = 98

  15. Mertsj
    • one year ago
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    The Theorem: An Angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc. 1/2 of196=98

  16. welshfella
    • one year ago
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    |dw:1434906511832:dw|

  17. welshfella
    • one year ago
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    - which makes m<ABC = 98 degrees this might be a round about way to do it though!!

  18. anonymous
    • one year ago
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    thank you !

  19. anonymous
    • one year ago
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    could you help me with another one?

  20. welshfella
    • one year ago
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    there you go Mertsj has a quick way

  21. anonymous
    • one year ago
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    If the measure of angle DEF is 65, what is the measure of arc DE ? http://media.apexlearning.com/Images/200701/18/df4742e6-e568-423e-bfe0-61f1985506e7.gif

  22. Mertsj
    • one year ago
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    Did you read the theorem I posted above?

  23. anonymous
    • one year ago
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    so do i just double 65

  24. welshfella
    • one year ago
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    use the theorem Mertsj quoted

  25. Mertsj
    • one year ago
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    yes

  26. anonymous
    • one year ago
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    thank you!

  27. Mertsj
    • one year ago
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    yw

  28. welshfella
    • one year ago
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    easy using that theorem

  29. Mertsj
    • one year ago
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    yep. That's what theorems are for. You prove something once and for all and then you don't have to reinvent the wheel for every similar problem.

  30. welshfella
    • one year ago
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    true - Its weird but we never touched arc measurements in Geometry in the UK - as I said I'm talking decades ago. Maybe they do now.

  31. Mertsj
    • one year ago
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    hopefully

  32. welshfella
    • one year ago
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    yes - i don't understand why they didn't

  33. anonymous
    • one year ago
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    how about another one?

  34. welshfella
    • one year ago
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    lol - this is a learning experience for me - OK

  35. anonymous
    • one year ago
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    In the diagram below, line AB and BC and are tangent to center O. What is the measure of arc ADC?

  36. anonymous
    • one year ago
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    so sorry

  37. anonymous
    • one year ago
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    http://media.apexlearning.com/Images/200701/18/ac3f47ed-9e85-4bd0-a3dc-1b67c4cc90fb.gif

  38. welshfella
    • one year ago
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    well as a full circle is 360 degrees arc ADC = 360 - 140

  39. anonymous
    • one year ago
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    so its 220

  40. welshfella
    • one year ago
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    yes

  41. anonymous
    • one year ago
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    thank you so much seriously!

  42. welshfella
    • one year ago
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    yw

  43. welshfella
    • one year ago
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    i learned something new myself

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