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Foreverisabell

  • 2 years ago

Find the measure of angle DCA if D is the incenter of the triangle ABC. Explain step by step please!

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  1. Foreverisabell
    • 2 years ago
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  2. Foreverisabell
    • 2 years ago
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    @ZeHanz this one.

  3. ZeHanz
    • 2 years ago
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    OK, the incenter is the intersection of the angle bisectors. You have two more angles now!

  4. Foreverisabell
    • 2 years ago
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    Also in this one, would y = 60?

  5. Foreverisabell
    • 2 years ago
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    Alright,

  6. ZeHanz
    • 2 years ago
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    y=60 degrees, if the triangle is supposed to be equilateral.

  7. Foreverisabell
    • 2 years ago
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    alright , now for the other problem, how do you find the measure of angle DCA?

  8. ZeHanz
    • 2 years ago
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    Better question, what are the measures of the angles CAB and ABC?

  9. Foreverisabell
    • 2 years ago
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    111 is the measure of ABC

  10. Foreverisabell
    • 2 years ago
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    I meant they all equal 180. But the missing one is 111.

  11. Foreverisabell
    • 2 years ago
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    which is c?

  12. ZeHanz
    • 2 years ago
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    DOn't know how you get these numbers. Remember: the lines drawn to the incenter are the angle bisectors. That means: angle CAB = 2*32 = ... angle ABC = 2*37 = ... Add these and subtract from 180 to get angle ACB.

  13. Foreverisabell
    • 2 years ago
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    yeah I got 42.

  14. ZeHanz
    • 2 years ago
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    That's right!

  15. Foreverisabell
    • 2 years ago
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    But why did you times 2 times each?

  16. Foreverisabell
    • 2 years ago
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    never mind I know why now.

  17. Foreverisabell
    • 2 years ago
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    So the measure of angle DCA would be 32 + 42 + what?

  18. ZeHanz
    • 2 years ago
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    Look at the drawing. The numbers are the measures of half the angles, because the lines to the incenter are the: angle b i s e c t o r s...

  19. ZeHanz
    • 2 years ago
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    DC is bisector of the angle we just found: 42 degrees, so 21 degrees is the measure of DCA!

  20. Foreverisabell
    • 2 years ago
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    But I thought the wanted the measure of the whole angle?

  21. Foreverisabell
    • 2 years ago
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    Measure of DCA = 21 degrees it seems really small?

  22. ZeHanz
    • 2 years ago
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    I'll make a drawing, hold on...

  23. Foreverisabell
    • 2 years ago
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    alright

  24. Foreverisabell
    • 2 years ago
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    Im pretty sure I understand now. They just want the measure of C?

  25. Foreverisabell
    • 2 years ago
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    Also I know that a squared + b squared = c squared. But this triangles does not show any angles so except 90 degrees. So Im not sure how to find x?

  26. Foreverisabell
    • 2 years ago
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    @ZeHanz

  27. ZeHanz
    • 2 years ago
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    If there is a right angle in the triangle (there is!) then a²+12²=20². You can work out a now.

  28. Foreverisabell
    • 2 years ago
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    Yeah But I can't seem to get it? how to get a?

  29. Foreverisabell
    • 2 years ago
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    @ZeHanz

  30. ZeHanz
    • 2 years ago
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    a²+144=400, so a²=?

  31. Foreverisabell
    • 2 years ago
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    16?

  32. ZeHanz
    • 2 years ago
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    a²=256, so a=16, right!

  33. Foreverisabell
    • 2 years ago
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    thank you!

  34. ZeHanz
    • 2 years ago
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    yw!

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