# Tedious $$I$$

Geometry Level 5

Given , a $$\triangle ABC$$ which is $$not-obtuse-angled$$ .

Now a square , a regular polygon of sides $$m$$ and another regular polygon of sides $$n$$ are constructed on sides of given triangle.

$$WLOG$$ let angle $$A=\alpha$$ ,angle $$B=\beta$$ ,angle $$C=\gamma$$. Such that $$\alpha \leq \beta <\gamma$$

Now centers of square and the 2 regular ploygons when joined form an $$equilateral$$ triangle .

Then find $$m+n+ \alpha - \beta + \gamma$$ .

Note : All angles are in degrees .

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