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Math Help - Angle of this isoscleles triangle.

  1. #1
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    Angle of this isoscleles triangle.

    Triangle ABC is isosceles with base AC. Points P and Q are respectively in CB and AB and such that AC = AP = PQ = QB. What is the degree of angle B?

    I have the solution, but I don't understand it.

    Represent the magnitude of angle B by m. Then, in order, we obtain angle QPB = m, angle AQP = 2m (??? from now on), angle QAP = 2m, angle QPA = 180 - 4m, angle APC = 3m, angle ACP = 3m. Since angle BCA = angle BAC = 3m, the sum of the angles in ABC is m + 3m + 3m = 7m = 180.
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  2. #2
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    Quote Originally Posted by chengbin View Post
    Triangle ABC is isosceles with base AC. Points P and Q are respectively in CB and AB and such that AC = AP = PQ = QB. What is the degree of angle B?

    I have the solution, but I don't understand it.

    Represent the magnitude of angle B by m. Then, in order, we obtain angle QPB = m, angle AQP = 2m (??? from now on), angle QAP = 2m, angle QPA = 180 - 4m, angle APC = 3m, angle ACP = 3m. Since angle BCA = angle BAC = 3m, the sum of the angles in ABC is m + 3m + 3m = 7m = 180.
    Here is the solution :
    Attached Thumbnails Attached Thumbnails Angle of this isoscleles triangle.-1.jpg  
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  3. #3
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    isosceles triangle

    Hello chengin,
    This is a geometry oddity.Triangle ABC cannot be constructed without knowing the angles and length of base.If given such a diagram and the given equalities the angles can be calculated.

    ABC= m
    QPC =m isosceles
    BQP = 180 - 2m triangle totals 180
    AQP =180-(180-2m) = 2m supplements
    QPA =180 -4m triangle totals 180
    APC=180-m-(180-4m) = 3m supplements
    ACP = 3m isosceles
    Triangle ABC has three angles m,3m,3m total 7m = 180 m=25.7
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  4. #4
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    Yep, quite an interesting triangle.

    If we let BC = k, then:
    equal sides AB and BC = k / [2SIN(90/7)]
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