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?

Question

Thank you!!

Answer 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°