Single correct option
Each interior angle of a regular polygon measures 156°. How many diagonals does the polygon have?
- A. 75
- B. 90
- C. 105
- D. 120
Show answer and solution
Answer: (B) 90
Exterior angle = 180° − 156° = 24°. Number of sides n = 360/24 = 15.
Number of diagonals = n(n − 3)/2 = 15 × 12/2 = 90.
Tip: it is always faster to go through the exterior angle, because the exterior angles of any convex polygon add up to 360°.
Number of diagonals = n(n − 3)/2 = 15 × 12/2 = 90.
Tip: it is always faster to go through the exterior angle, because the exterior angles of any convex polygon add up to 360°.
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