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Problem of the Week 1136

A Square Angle

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Let ABCD be a unit square with A at the lower left, B at lower right, C at upper right, and D at upper left. From A and B, draw lines into the square making 15° angles with the base AB, and let E be their intersection point.

What is the measure of ∠CED?

Of course, an exact proof is wanted, not a numerical approximation based on trigonometry, since the latter would not be a rigorous proof.

© Copyright 2010 Stan Wagon. Reproduced with permission.

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1 November 2010