Numerical answer
Each interior angle of a regular polygon measures 150°. How many diagonals does the polygon have?
Show answer and solution
Answer: 54
Each exterior angle = 180° − 150° = 30°. Since exterior angles sum to 360°, the number of sides n = 360/30 = 12.
Number of diagonals = n(n − 3)/2 = 12 × 9/2 = 54.
Tip: Always go via the exterior angle (360/n) — it is quicker than using (n − 2) × 180/n.
Number of diagonals = n(n − 3)/2 = 12 × 9/2 = 54.
Tip: Always go via the exterior angle (360/n) — it is quicker than using (n − 2) × 180/n.
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