Math

In the diagram triangle xyz is isosceles with xy=xz.Also,point w is on xz so that xw=wy=yz.The measure of angle xyw is

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  1. We have 3 isosceles triangles
    In triangle xyw, xw = yw, as stated
    mark angle x = angle xyw = a
    in triangle xyz, xy = xz, as stated
    mark angle xyz = angle xzy = b

    in triangle wyz, yw = yz, as stated
    mark angle wyz = b-a

    also angle ywz is an exterior angle in triangle xyw,
    so angle ywz = 2a

    so back to triangle wyz,
    b = 2a, isosceles triangle
    and
    2a + b-a + b = 180°
    a + 2b = 180
    a + 2(2a) = 180
    5a = 180
    a = 36°
    then b = 72°

    and angle xyw = 36°

    aside:
    This particular configuration is considered the "golden triangle"
    note that cos 36° = (1+√5)/4
    which is 1/2 the Golden Ratio.

    Also see "Golden Ratio" and "golden rectangle"

    Isn't Math wonderful??

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  2. xyz

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  3. Good

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  4. Thanks

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