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The sum of the interior angles of a regular polygon is 1260 degrees. Find the number of diagonals that can be drawn in the polygon.

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Answer to a math question The sum of the interior angles of a regular polygon is 1260 degrees. Find the number of diagonals that can be drawn in the polygon.

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Hester
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116 Answers
Solution:
1. Given:
- Sum of interior angles of the polygon: 1260 degrees

2. Use the formula for the sum of interior angles of a polygon:
180(n-2) degrees

3. Set the given sum equal to the formula and solve for n:
180(n-2) = 1260
n-2 = \frac{1260}{180}
n-2 = 7
n = 9

4. We now know the polygon has 9 sides.

5. Use the formula for the number of diagonals in a polygon:
- The number of diagonals D in an n-sided polygon is given by:
D = \frac{n(n-3)}{2}

6. Substitute n = 9 into the formula:
D = \frac{9(9-3)}{2}
D = \frac{9 \cdot 6}{2}
D = \frac{54}{2}
D = 27

The number of diagonals is 27.

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