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Two plane mirrors are separated by $120^{\circ},$ as the drawing illustrates. If a ray strikes mirror $M_{1}$ at a $65^{\circ}$ angle of incidence, at what angle $\theta$ does it leave mirror $M_{2} ?$

$55^{\circ}$

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in this problem. We flocked to play mirrors and one can empty an empty space at an angle upon 20 begins from M one German kick and we've got a lightning striking and one at an idol of incidents of 65 degrees. And it's being affected back and then striking and do and then being reflected back again and leaving at an angle of perfection off data which we have flying on where they were going to do that, using some simple language, Poverty's on. We can start by saying that both the angle Oh, and with inspection right here, when the Reaper strikes, someone is going to be equal, um, to the angle of incidence. So the animal protection is also work to be 65 and then we can see. You can see that, um, this triangle right here. Uh, we know one of the islands. It's 1 20 We can figure out this angry by noticing that this line right here pointing normal so we can subtract 65 from 90 which gives us this anger as when five degrees. And we know that, um, this small triangle right here the told in some of the sum of the angles. So 12 and three opposition. Some amount of speed should be equal to 1 80 So if you subtract 1 20 plus 45 um, from 1 80 uh, that would give us this island right here, which should be equal. Do 35 degrees using that. Begin again, use the fact we can again use the fact that best, right hands and Norma to this total, this total angle is 90 between the mirror and the normal. So if you have DR 35 from landing, we get this anger, which is 55. And you can see finally that, um, this 55 is actually the angle of incidence off are rare. Uh, and because this is a plane mirror, it should be equal to the angle of reflection. So the angler mystery leaves. I m do so that Seita should be equal to 55