Geometry

Lines l and m have an intersection at point O and any reflection in l followed by a reflection in m results in a rotation about point O of 136 degrees. What is the acute angle between l and m?
Thank you!!

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  1. Draw any two lines l and m to intersect at P
    Pick any point P, not on either line
    Then let P1 be the reflection of P in line l, and P2 the reflection of P1 in m
    We now have two isosceles triangles, OP2P1 and OPP1
    Also m will be a right - bisector of P1P2 at S and l will be a right - bisector of PP1 at T

    l and m will also be the angle bisectors in those two isosceles triangles, thus
    angle(P2OP) = 2 x angle(SOT)
    136 = 2 x angle (SOT)
    angle (SOT) = 68°

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