Question
Download Solution PDFIf the number of diagonals in a regular polygon is 9, then what is the sum of all the interior angles of the polygon?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Number of diagonals = 9
Formula used:
Number of diagonals = n(n - 3) / 2
Sum of interior angles = (n - 2) × 180°
Calculation:
⇒ n(n - 3)/2 = 9
⇒ n(n - 3) = 18
⇒ n2 - 3n - 18 = 0
⇒ (n - 6)(n + 3) = 0
⇒ n = 6 (since n > 0)
Sum of interior angles = (6 - 2) × 180 = 4 × 180 = 720°
∴ Sum of all interior angles = 720°
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