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Math Help - Angles Problem

  1. #1
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    Angles Problem

    Angles Problem-img_0103.jpg

    Here are two mirrors OD and OE the angle between them is "alpha"

    The question is to find angle "beta"

    Help Please!
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  2. #2
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    Re: Angles Problem

    Angle-chasing usually works:

    \angle OBA = 90-\alpha

    \angle DBC = 90-\alpha (due to symmetry)

    \angle ABC = 2 \alpha (since OBA + DBC + ABC = 180 deg)

    \angle ACB = 90 - 2\alpha

    \angle EC(D) = 90 - 2\alpha (also due to symmetry)

    \angle BC(D) = \beta = 4 \alpha (since ACB + EC(D) + BC(D) = 180 deg)
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  3. #3
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    Re: Angles Problem

    thanks very much but why are <OBA and <DBC equal? they are not similar triangles please explain ;(
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  4. #4
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    Re: Angles Problem

    It's because the ray reflects at point B, so the angle of incidence equals the angle of reflection.
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