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

In a regular pentagon inscribed in a circle with center O what is the measure of angle x?

figure

Draw the radius OA:

figure

Because the polygon is regular, the angle ∠COB is:

equation

The triangle AOB is isosceles, since OA and OB are radii of the same circle. Therefore:

equation

Since:

equation

Use the fact that the angles of a triangle add up to 180° to find:

equation