In an equilateral triangular mirror room a laser is shot from the top vertex down to the base. The light ray bounces three times to return to the same base point. What is the angle α?

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## Solution

The angle α is 30°.

Unfold reflections to five triangles, then left red triangle rotates to right about E by 120° and H is on the intersection with the circle through AEJ (angle at E and H is 120°). Then angle HAJ is 15° (half angle on AE which is 30°) so black angle is 105° and α = 2(105-90) = 30°.