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This problem trains for: SAT-I, AMC-8, GMAT.

In a regular pentagon (convex polygon with five congruent sides and five congruent angles), what is the angle at the apex of the shaded triangle?

figure

Compute the interior angle of the regular pentagon using the formula for the sum of the interior angles of a convex polygon with N=5:

figure

equation

equation

Since the interior angle of the regular pentagon is 108°, and the triangle AED is isosceles:

equation

Similarly,

equation

and

equation