# Good analytical geometry from

Geometry Level 5

In the figure below,

$$ABCD$$ is a square. $$E$$ and $$F$$ are points on $$BC$$ and $$CD$$ respectively such that $$AE$$ cuts the diagonal $$BD$$ at $$G$$ and $$FG$$ is perpendicular to $$AE$$. $$K$$ is a point on $$FG$$ such that $$AK = EF$$. Find the measure of angle $$EKF$$ in degrees.

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