There is an equilateral triangle,ABC,inscribed in a circle with center D.what is the smallest angle you can rotate triangle ABC around D so that the image of A is B?

Question

A.60°

B.90°

C.120°

D.180°

Answer 1

Draw and label a diagram!

All angles in an equilateral triangle measure 60°

All angles subtend arcs of 120°.

B must move through 120° to replace A.

Answer 2

I'm assuming your question is: what is the smallest angle you could rotate the system about D to get the original system. That is, imagine that you have a cut out equilateral triangle, and you affix it to a wall by inserting a pushpin in the very center. What angle would you have to rotate it by so that it looks the exact same?

Well if you were to rotate it all the way around, it would be 360 degrees. Obviously in that case it would look the same. But you don't need to rotate it all the way around, you can just rotate one vertex of the triangle to where the adjacent vertex is at the start. That's the angle you need to figure out.