Question
Find the sum of the measures of the interior angles of each convex polygon: 180(n-2) Pentagon 540 2 Numeric 1 point Find the sum of the measures of the interior angles of each convex polygon: 180(n-2) Heptagon Type your answer...
Ask by Robbins Evans. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The sum of the interior angles of a heptagon is 900 degrees.
Solution
To find the sum of the measures of the interior angles of a heptagon:
Use the formula:
\[ \text{Sum of interior angles} = 180(n - 2) \]
where \( n \) is the number of sides.
For a **heptagon** (\( n = 7 \)):
\[ \text{Sum} = 180(7 - 2) = 180 \times 5 = 900 \text{ degrees} \]
**Answer:**
900
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Simplify this solution Beyond the Answer
A heptagon has 7 sides, so to find the sum of the measures of the interior angles, you would use the formula 180(n-2), where n is the number of sides. Plugging in 7 for n, you get 180(7-2) = 180(5) = 900 degrees. So, the sum of the interior angles of a heptagon is 900 degrees! And just to be extra clear, the formula comes from the fact that you can divide any polygon into triangles. Since each triangle has interior angles summing to 180 degrees, you multiply the number of triangles (which is the number of sides minus two) by 180 to get the total!
