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Math Help - Angle Measurements

  1. #1
    Mel
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    Angle Measurements

    Find x, y and z in the triangle within the circle.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Mel View Post
    Find x, y and z in the triangle within the circle.
    Hi Mel,

    Angle x is 1/2 the sum of its intercepted arcs or 1/2 (30 + 134).

    Arc BE measures 118 because it is twice the measure of the inscribed angle D which is 59 degrees. Therefore, angle y is 1/2 the measure of arc BE because it is also an inscribed angle. Angle y is the same measure as angle D because they both intercept the same arc BE.

    To find the measure of arc DF we have to subtract the other arcs from 360. So 360 - 134 - 118 - 30 = 78 degrees for arc DF. And angle z is 1/2 of that.
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