Question

Triangle ABC is an equilateral triangle.Find the angle of rotation that maps A to B

Answer 1

The sum of the inner angles of any triangle is always 180°, i.e. you have

`\alpha + \beta + \gamma = 180`

In the particular case of an equilater triangle, all three angles are the same, so

`\alpha = \beta = \gamma`

and the expression becomes

`\alpha + \beta + \gamma = \alpha + \alpha + \alpha = 3\alpha = 180`

which implies
`\alpha = 60`

So, if you rotate the triangle with respect to its center by 60 degrees, the triangle will map into itself. In particular, if you want point A to be mapped into point B, you have to perform a counter clockwise rotation of 60 degrees with respect to the center of the triangle.

Of course, this is equivalent to a clockwise rotation of 120 degrees.

Finally, both solutions admit periodicity: a rotation of 60+k360 degrees has the same effect of a rotation of 60 degrees, and the same goes for the 120 one (actually, this is obvisly true for any rotation!)