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Thread: Triangle Help

  1. #1
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    Triangle Help

    Please explain why the third answer is correct. Thank you.

    PS - You can click on the picture to see it full size.
    Attached Thumbnails Attached Thumbnails Triangle Help-geometryproblem1.jpg  
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  2. #2
    MHF Contributor red_dog's Avatar
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    We have $\displaystyle \widehat{RQS}=\widehat{RSQ}=\alpha$

    $\displaystyle \widehat{TSU}=\widehat{TUS}=\beta$

    If we know both $\displaystyle \alpha$ and $\displaystyle \beta$ then we can find x. For this we have:

    $\displaystyle \alpha+x+\beta=180^{\circ}$ and

    $\displaystyle 180^{\circ}-2\alpha+180^{\circ}-2\beta=90^{\circ}$

    and we get $\displaystyle x=45^{\circ}$

    But if we know just $\displaystyle \alpha$ (or just $\displaystyle \beta$) then we can't find x.
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