QQuestionMathematics
QuestionMathematics
What is the sum of the measures of the exterior angles of the polygon shown below? If necessary, round to the nearest tenth
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Answer
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Step 1
First, let's recall that the sum of the measures of the exterior angles of any convex polygon is always 360 degrees. This is because the sum of the measures of the interior angles of a convex polygon is (n- 2) * 180 degrees, where n is the number of sides. The exterior angle at each vertex is the supplement of the interior angle, so the sum of the measures of the exterior angles is [(n- 2) * 180] + n * 180 = 360n.
Step 2
In this problem, we are given a regular polygon, which means all sides and angles are congruent. A regular dodecagon has 12 sides, so we can substitute n = 12 into the formula: \text{Sum of exterior angles} = 360 \times 12 = \boxed{4320}
Final Answer
The sum of the measures of the exterior angles of the dodecagon is approximately 4320 degrees.
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