suppose two mirrors are placed at 60 degree a line reflected from its surface forms an angle so what will be the measurement of that angle?  

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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Hello!

I believe the mirrors are plane and a ray reflects from both of them.

Denote the angle between the mirrors as `alpha` and the first angle of incidence as `beta.` And we know that an angle of incidence is equal to an angle of reflection. Now please look at the picture.

The angle of incidence is `beta,` then the angle of the first reflection `BAO`  is also `beta.` The second angle of incidence `ABB_1` is equal to `alpha+beta` as an external angle of the triangle `OBA.` Then the second angle of reflection is also `alpha+beta,` and the angle between them (denoted `gamma`) is `pi-2(alpha+beta).`

Now consider the triangle `ABC.` The angle `C` is the angle in question (the angle between the continuations of the original ray and the twice reflected ray). And it is equal to

`pi-[(pi-2(alpha+beta))+2beta]=pi-[pi-2alpha]=2alpha`

(the angle `OAC` is also `beta` as a vertical to the original angle).

 

So this angle doesn't depend on an angle of incidence.

If an angle `beta` would be greater, the picture will change somewhat but the answer will remain the same.

For our case `alpha`=60° and the answer is 120°.

 

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