Question:
The number of diagonals of a polygon with 15 sides is
The number of diagonals of a polygon with 15 sides is
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Each vertex connects to \( n-3 \) vertices to form diagonals.
Updated On: May 1, 2026
- \( 90 \)
- \( 45 \)
- \( 60 \)
- \( 70 \)
- \( 10 \)
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The Correct Option is A
Solution and Explanation
Concept:
Number of diagonals in an \( n \)-sided polygon:
\[
\frac{n(n-3)}{2}
\]
Step 1: Identify number of sides.
\[ n = 15 \]
Step 2: Substitute into formula.
\[ \frac{15(15-3)}{2} \]
Step 3: Simplify.
\[ = \frac{15 \cdot 12}{2} \]
Step 4: Compute result.
\[ = 15 \cdot 6 = 90 \]
Step 5: Final answer.
\[ 90 \]
Step 1: Identify number of sides.
\[ n = 15 \]
Step 2: Substitute into formula.
\[ \frac{15(15-3)}{2} \]
Step 3: Simplify.
\[ = \frac{15 \cdot 12}{2} \]
Step 4: Compute result.
\[ = 15 \cdot 6 = 90 \]
Step 5: Final answer.
\[ 90 \]
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