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anonymous

  • one year ago

Kite DCFE is inscribed in circle A shown below. If the measure of is 232°, what is the measure of ∠ DEF? (5 points)

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  1. anonymous
    • one year ago
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  2. mathstudent55
    • one year ago
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    The measure of what is 232 deg? The info is missing in your post.

  3. anonymous
    • one year ago
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    I know that a circle = 360 and that 360 - 232 = 128 but 128 is the arc of angle FDE not DEF? I also know that the inscribed angles theorem means that angles = 1/2 the value of their intercepted arcs.

  4. anonymous
    • one year ago
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    Oh oops hold on

  5. anonymous
    • one year ago
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    The measure of DEF @mathstudent55

  6. mathstudent55
    • one year ago
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    Angle DEF?

  7. anonymous
    • one year ago
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    Yes.

  8. mathstudent55
    • one year ago
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    Arc DEF?

  9. anonymous
    • one year ago
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    No angle DEF

  10. mathstudent55
    • one year ago
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    Wait. We are looking for the measure of angle DEF. That much I see in your post. What measures 232 deg? Is it arc DEF or something else?

  11. mathstudent55
    • one year ago
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    |dw:1434041246519:dw|

  12. anonymous
    • one year ago
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    The question is this: If the measure of ARC DE is 232°, what is the measure of ∠ DEF? I have shared an imagine. This is as much as I know: I know that a circle = 360 and that 360 - 232 = 128 but 128 is the arc of angle FDE not DEF? I also know that the inscribed angles theorem means that angles = 1/2 the value of their intercepted arcs.

  13. mathstudent55
    • one year ago
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    |dw:1434041331681:dw|

  14. anonymous
    • one year ago
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    Naw, its the other way from DE. Sorry for the confusion

  15. mathstudent55
    • one year ago
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    Arc DE cannot be 232 deg because arc FE is congruent to arc FE, and just that would total more than 360 deg. Is it measure of arc DEF that is 232?

  16. anonymous
    • one year ago
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    Yes, sorry

  17. anonymous
    • one year ago
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    @mathstudent55 Yes, arc DEF

  18. mathstudent55
    • one year ago
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    Ok. Remember a kite is symmetric, so these arcs are congruent. See pic below. |dw:1434041802642:dw|

  19. mathstudent55
    • one year ago
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    If arc DEF measures 232, arcs DE and FE measure half that much.

  20. anonymous
    • one year ago
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    Why's that?

  21. mathstudent55
    • one year ago
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    Also, because of symmetry of a kite, the angles below are congruent. |dw:1434041934430:dw|

  22. anonymous
    • one year ago
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    Ahhhh I see

  23. anonymous
    • one year ago
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    Okay

  24. mathstudent55
    • one year ago
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    Arc measures below: |dw:1434042008754:dw|

  25. mathstudent55
    • one year ago
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    Angle DEF measures twice angle DEC. An inscribed angle measure half of its tended arc.

  26. anonymous
    • one year ago
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    Wow

  27. anonymous
    • one year ago
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    But wait

  28. anonymous
    • one year ago
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    64+64+112 = 244

  29. anonymous
    • one year ago
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    not 232

  30. mathstudent55
    • one year ago
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    OK. Now that I know what the 232 deg refers to, let's start from the beginning.

  31. mathstudent55
    • one year ago
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    You start like this. |dw:1434042759323:dw|

  32. mathstudent55
    • one year ago
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    You were correct to subtract 232 from 360. You get this: |dw:1434042831738:dw|

  33. mathstudent55
    • one year ago
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    |dw:1434042874732:dw|

  34. mathstudent55
    • one year ago
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    Angle DEF is the inscribed angle of an arc of measure 128, so angle DEF measures half of 128, which is 64.

  35. anonymous
    • one year ago
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    OH MY GOODNESS! Okay I get everything now, I didnt realize that that was DEF I thought ANGLE DEF was from point D to E to F clockwise I get it now

  36. anonymous
    • one year ago
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    xD

  37. anonymous
    • one year ago
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    @mathstudent55 Thanks, you get a medal :) well-deserved

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

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