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Thread: triangle length vs angles

  1. #1
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    triangle length vs angles

    What is the value of x in the attached?
    all I can think of is EDC = DCA which makes DE also 5 but then I am stuck. The answer should be 10
    triangle length vs angles-20181108_212012-2.jpg
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  2. #2
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    Re: triangle length vs angles

    Quote Originally Posted by ketanco View Post
    What is the value of x in the attached?
    all I can think of is EDC = DCA which makes DE also 5 but then I am stuck. The answer should be 10
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    Yes angle EDC = angle DCA (alternate angles)
    Also, angle DCA = angle ECD (because CD bisects angle BCA)

    This makes triangle DCE an isosceles triangle and so DE = 5.


    Now look at triangle DBE:


    angle DBE = angle ACB (since triangle ABC is isosceles)


    Also angle ACB = angle DEB (corresponding angles)


    So angle DEB = angle DBE, making DBE an isosceles triangle and therefore DB = DE = 5.


    Now AC = AB = AD+DB = 6+5 = 11. (I don't agree that the answer is 10, unless EC=4 rather than 5.)
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  3. #3
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    Re: triangle length vs angles

    Quote Originally Posted by Debsta View Post
    Yes angle EDC = angle DCA (alternate angles)
    Also, angle DCA = angle ECD (because CD bisects angle BCA)

    This makes triangle DCE an isosceles triangle and so DE = 5.


    Now look at triangle DBE:


    angle DBE = angle ACB (since triangle ABC is isosceles)


    Also angle ACB = angle DEB (corresponding angles)


    So angle DEB = angle DBE, making DBE an isosceles triangle and therefore DB = DE = 5.


    Now AC = AB = AD+DB = 6+5 = 11. (I don't agree that the answer is 10, unless EC=4 rather than 5.)
    thanks a lot
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