A regular polygon has each interior angle measuring 150°. Find the number of its sides.
12
For a regular polygon with \(n\) sides, each interior angle is
\(\dfrac{(n-2) \times 180^\circ}{n}\)
Set up and solve:
\(\dfrac{(n-2) \times 180}{n} = 150\)
\(180n - 360 = 150n \;\Longrightarrow\; 30n = 360 \;\Longrightarrow\; n = 12\)
Cross-check (using exterior angle): Each exterior angle = \(180 - 150 = 30^\circ\), and the exterior angles sum to 360°, giving \(n = 360/30 = 12\).
Hence the polygon has 12 sides — option (2).
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