Question
What is the measure of each angle of a regular 17-gon? If necessary, round to the nearest tenth.
Ask by Phillips Barrett. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Each angle of a regular 17-gon measures approximately 158.8 degrees.
Solution
To find the measure of each angle of a regular 17-gon, we can use the formula for the sum of interior angles of a polygon:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
where \( n \) is the number of sides of the polygon.
For a regular 17-gon, the number of sides is 17. Plugging this into the formula, we get:
\[ \text{Sum of interior angles} = (17 - 2) \times 180^\circ = 15 \times 180^\circ = 2700^\circ \]
Since the polygon is regular, all interior angles are equal. To find the measure of each angle, we divide the sum of interior angles by the number of sides:
\[ \text{Measure of each angle} = \frac{2700^\circ}{17} \]
Let's calculate this value.
Calculate the value by following steps:
- step0: Calculate:
\(\frac{2700}{17}\)
The measure of each angle of a regular 17-gon is approximately 158.8 degrees. Rounding to the nearest tenth, the measure of each angle is 158.8 degrees.
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Simplify this solution Bonus Knowledge
To find the measure of each interior angle of a regular 17-gon, you can use the formula: \((n-2) \times 180^\circ / n\), where \(n\) is the number of sides. So, for a 17-gon, it's \((17-2) \times 180^\circ / 17\), which simplifies to \(15 \times 180^\circ / 17\), resulting in approximately \(158.8^\circ\) for each angle when rounded to the nearest tenth. Imagine hosting a polygon party! Each of the 17 guests (the vertices) comes with a unique angle of about \(158.8^\circ\) to share. As they mingle and form their relationships, the regularity of their angles ensures that no one feels left out, just like in a perfectly symmetrical dance!
