Answer:
15°
Explanation:
For consecutive vertices P, Q, R of a regular dodecagon, you want the measure of angle PRQ.
Exterior angle
The exterior angle at any vertex of a regular 12-sided polygon measures ...
360°/12 = 30°
Triangle
The exterior angle just figured is equal to the sum of the base angles of the isosceles triangle PQR. That is, angle R is ...
R = 30°/2 = 15°
The size of angle PQR is 15°.
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Additional comment
The sum of exterior angles of any convex polygon is 360°. It is often easy to figure the measure of an exterior angle using this relation.
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