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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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

180(n-2) = 1260

n-2 = \frac{1260}{180}

n-2 = 7

n = 9

4. We now know the polygon has

sides.

5. Use the formula for the number of diagonals in a polygon:
- The number of diagonals

in an

-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

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