What is the sum of the interior angles of a regular polygon with 13 sides?
A. 2340
B. 2520
C. 2970
D. 1980
Answer (2)
Recall the formula for the sum of interior angles of a polygon: ( n − 2 ) × 18 0 \tcirc .
Substitute n = 13 into the formula: ( 13 − 2 ) × 18 0 \tcirc .
Calculate the result: 11 × 18 0 \tcirc = 198 0 \tcirc .
The sum of the interior angles is 1980 .
Explanation
Problem Analysis We are asked to find the sum of the interior angles of a regular polygon with 13 sides.
Formula Recall The formula for the sum of the interior angles of a polygon with n sides is given by: ( n − 2 ) × 18 0 \tcirc
Substitution In our case, the polygon has 13 sides, so n = 13 . Substituting this into the formula, we get: ( 13 − 2 ) × 18 0 \tcirc = 11 × 18 0 \tcirc
Calculation Now, we perform the multiplication: 11 × 180 = 1980
Conclusion Therefore, the sum of the interior angles of a 13-sided polygon is 198 0 \tcirc .
Examples
Understanding the sum of interior angles is crucial in architecture and design. For instance, when designing a building with a polygonal base, architects need to calculate the angles to ensure structural integrity and aesthetic appeal. Knowing the sum of interior angles helps in creating precise blueprints and ensuring that the building fits the intended design, making spaces functional and visually harmonious.
The sum of the interior angles of a regular polygon with 13 sides is calculated using the formula ( n − 2 ) × 180 where n is the number of sides. After substitution and calculation, it results in 198 0 ∘ . Therefore, the correct answer is option D. 1980.
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