Question
QUESTION 6 Polygons have exterior angles that add up to \( 360^{\circ} \). It depends on number of sides It depends on if the shape is regular Always Never
Ask by Griffin Sandoval. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The sum of the exterior angles of any polygon is always \(360^\circ\).
Solution
To solve the problem, we first recall the following fact:
- For any polygon, the sum of the measures of the exterior angles, one at each vertex, is always \(360^\circ\).
This fact holds irrespective of:
- The number of sides of the polygon.
- Whether the polygon is regular (all sides and angles are congruent) or irregular.
Thus, the correct answer is:
**Always**
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Simplify this solution The Deep Dive
Guess what? The exterior angles of a polygon, regardless of the number of sides or whether it's regular or irregular, always add up to \( 360^\circ \)! So whether you're wrangling with a triangle or a dodecagon, the magic number remains the same. It's like a quirky rule of geometry that keeps things consistent! Now, if you're exploring this in a real-world context, think of a stop sign. It's an octagon with 8 sides, and even when it comes to calculating the angles between the arms of the sign, they too will contribute to that lovely total of \( 360^\circ \). So every sharp turn is part of that geometric dance!
