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What is the sum of the interior angles of a 25-gon?

Ask by Gordon Evans. in the United States
Mar 11,2025

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Answer

The sum of the interior angles of a 25-gon is 4140 degrees.

Solution

1. For any \( n \)-gon, the sum of the interior angles is given by: \[ S = (n - 2) \times 180^\circ \] 2. For a 25-gon, substitute \( n = 25 \): \[ S = (25 - 2) \times 180^\circ = 23 \times 180^\circ \] 3. Multiply: \[ 23 \times 180 = 4140^\circ \] Thus, the sum of the interior angles of a 25-gon is \(4140^\circ\).

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To find the sum of the interior angles of a 25-gon, you can use the formula: (n - 2) × 180°, where n is the number of sides. For a 25-gon, this would be (25 - 2) × 180°, which equals 23 × 180° = 4140°. So, the sum of the interior angles of a 25-gon is 4140 degrees! Here's a fun fact: If you think about a polygon as a full pizza, each slice represents an angle! So, for a 25-gon, you have 25 slices, and they all add up to 4140 degrees of deliciousness! Now, that’s a pizza party worth celebrating! If you’re curious about how different polygons stack up angle-wise, consider looking at polygons with fewer sides. A triangle has 180° (3-gon), a square has 360° (4-gon), and things get more interesting as you go up in sides. Exploring the relationship between sides and angles can be a delightful math adventure!

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