k is the center of tangent circle so what is the angle of A.

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Can I assume that when you say "tangent circle" you mean that I could use a compass to draw a circle centered at point K that would touch all three "corners" of the triangle? If so, then what you've got is an equilateral triangle, which has all three sides the same and all three angles the same. Since a triangle has 180 degrees in total, if there are three angles all the same, then each is 60 degrees - including angle A, at the top of the triangle.

I hope this helps

- Steve J