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Math Help - HELP!!! ratios! ack!!

  1. #1
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    HELP!!! ratios! ack!!

    I reallly wanna go to bed but I need to get my homework done and I'm absolutely stuck on this one.

    "The measures of two angles are in the ratio 5:3. The measure of the larger angle is 30 greater than half the difference of the angles. Find the measure of each angle."

    I seriously cannot make left or right of this question. Please help!!!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by A dumb person View Post
    I reallly wanna go to bed but I need to get my homework done and I'm absolutely stuck on this one.

    "The measures of two angles are in the ratio 5:3. The measure of the larger angle is 30 greater than half the difference of the angles. Find the measure of each angle."

    I seriously cannot make left or right of this question. Please help!!!
    Let \alpha represent the smaller angle, and let \beta represent the larger angle.

    Thus, we see that \frac{\beta}{\alpha}=\frac{5}{3}

    Now, the larger angle is 30 more than half of the difference of the angles. This means that \beta=30+\tfrac{1}{2}(\beta-\alpha)

    We can now solve this system of equations:

    \left\{\begin{aligned}30+\tfrac{1}{2}(\beta-\alpha)&=\beta\\\tfrac{3}{5}\beta&=\alpha\end{alig  ned}\right.

    Try to take it from here. It shouldn't be that bad.

    I hope this makes sense!

    --Chris
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