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Find the measure of a single exterior angle of a regular heptagon. If necessary, round to the nearest tenth. Answer Atumptreut of?

Ask by Daniel Willis. in the United States
Mar 11,2025

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Answer

Each exterior angle of a regular heptagon is approximately \(51.4^\circ\).

Solution

1. We know that the sum of the exterior angles of any polygon is \(360^\circ\). 2. Since the heptagon is regular (all sides and angles are equal), each exterior angle is given by \[ \text{Exterior Angle} = \frac{360^\circ}{7}. \] 3. Calculating the value, we have \[ \frac{360}{7} \approx 51.4286^\circ. \] 4. Rounding to the nearest tenth, the measure of one exterior angle is approximately \[ 51.4^\circ. \]

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The Deep Dive

To find the measure of a single exterior angle of a regular heptagon (a 7-sided polygon), you can use the formula for the exterior angles of any polygon, which is 360° divided by the number of sides. So, for a heptagon, you would calculate 360° ÷ 7, which equals approximately 51.4°. Therefore, the measure of a single exterior angle of a regular heptagon is about 51.4°. Now, here’s a fun fact: the heptagon is often associated with artistic compositions and symbols, including the seven sides that can represent the seven wonders of the world! People have been fascinated by polygons for centuries, using them in everything from architecture to art. For a practical application, when designing objects or patterns, understanding the angles of shapes like the heptagon can help create balanced and aesthetically pleasing designs. Whether you're crafting a piece of jewelry or designing a building, these angles ensure your work not only looks good but is structurally sound too!

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