Rotating a Square

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In the figure above, AC passes through the center of the square ABCD, and CE is perpendicular to AC. What is the minimum number of degrees the square must be rotated so that BC will be parallel to EC?

Review: Rotating a Square


Explanation

In this question, if this square were a handle or a doorknob, we would be grabbing it and turning it left or counter-clockwise just a bit, until the side BC comes to rest along the line segment EC, which we imagine has not rotated. But how much? The angle ACE is a right angle, so its degree measure is 90. Meanwhile, the angle ACB must be 45, because the line AC bisects the angle BCD. We can conclude that the side BC bisects the right angle of the dotted line and must be turned 45 degrees to reach EC.

The correct answer is (A).


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