BTGmoderatorLU wrote:
If ABCD is square and both AED and CDF are equilateral triangles, what is the angle FGC?
$$A.\ 45^o$$
$$B.\ 50^o$$
$$C.\ 60^o$$
$$D.\ 75^o$$
$$E.\ 80^o$$
Because triangles ADE and CDF are equilateral, we get:
Because triangle AED is equilateral, DE = AD.
Because ABCD is a square, AD = CD.
.Thus, DE=CD, with the result that triangle CDE is isosceles:
Similar reasoning can be used to show that triangle ADF is isosceles:
Since the angles inside triangle AEG must sum to 180, we get:
Thus, angle FGC = 60.
The correct answer is
C.
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