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Math Help - Please Help! angle word problem

  1. #1
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    Please Help! angle word problem

    Please help me on this prob, it is really hard! for me of course, I really need it urgently

    1.) The sum of the measures of two obtuse angles is 215. The sum of the 3/5 of the supplement of the smaller angle and 2/3 of the supplement of the larger angle is 91. Find the measures of the angle.

    *note* if 215 wont work out, try using 2/5, I'm not sure because the writing of my classmate is confussing

    thanks........
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  2. #2
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    Quote Originally Posted by Aussieboy View Post
    Please help me on this prob, it is really hard! for me of course, I really need it urgently

    1.) The sum of the measures of two obtuse angles is 215. The sum of the 3/5 of the supplement of the smaller angle and 2/3 of the supplement of the larger angle is 91. Find the measures of the angle.

    *note* if 215 wont work out, try using 2/5, I'm not sure because the writing of my classmate is confussing

    thanks........
    Call the first angle A and the second angle B. Let A < B.

    We know that
    A + B = 215
    \frac{3}{5}(180 - A) + \frac{2}{3}(180 - B) = 91

    The second equation simplifies a bit:
    108 - \frac{3}{5}A + 120 - \frac{2}{3}B = 91

    \frac{3}{5}A + \frac{2}{3}B = 137

    The first equation says:
    B = 215 - A

    So inserting this into the second equation gives:
    \frac{3}{5}A + \frac{2}{3}(215 - A) = 137

    \frac{3}{5}A + \frac{2}{3}(215) - \frac{2}{3}A = 137

    \left ( \frac{3}{5} - \frac{2}{3} \right ) A + \frac{2}{3}(215) = 137

    \left ( \frac{9 - 10}{15} \right ) A = - \frac{2}{3}(215) + 137

    \left ( \frac{ -1}{15} \right ) A = - \frac{2}{3}(215) + 137

    A = 15 \left ( \frac{2}{3}(215) - 137 \right )

    A = 2150 - 2055

    A = 95 (Which is, in fact, an obtuse angle.)

    Thus
    B = 215 - 95 = 120

    So A = 95 degrees and B = 120 degrees.

    -Dan
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