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Question What is the sum of the measures of the exterior angles of a triangle? If necessary, round to the nearest tenth. Answer Attempt 1 out of 2

Ask by Ross Gibbs. in the United States
Mar 11,2025

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The sum of the exterior angles of a triangle is 360.0 degrees.

Solución

To find the sum of the measures of the exterior angles of a triangle, we can follow these steps: 1. **Understanding Exterior Angles**: The exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side. Each exterior angle is equal to the sum of the two opposite interior angles. 2. **Sum of Interior Angles**: The sum of the interior angles of a triangle is always \(180^\circ\). 3. **Calculating the Sum of Exterior Angles**: For any polygon, the sum of the exterior angles is always \(360^\circ\), regardless of the number of sides. This is true for triangles as well. Thus, the sum of the measures of the exterior angles of a triangle is: \[ 360^\circ \] Since the problem does not require rounding, the final answer is: **360.0**

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The sum of the measures of the exterior angles of a triangle is always 360 degrees, regardless of the shape of the triangle. This is a fascinating property of polygons that holds true for any polygon with any number of sides. So, no need to round—just enjoy the consistent geometry! As a fun way to remember this, picture a triangle as a little sailboat cutting through the waves. If you were to unfurl three sails (one for each angle), as you turn each corner, your sails would open up to the winds of 360 degrees all around you, creating a full circle of opportunities!

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