A designer creates a regular polygonal clock with each internal angle 150°. How many sides does it have?
12
We are told the interior angle of a regular polygon and must find the number of its sides.
Given: each interior angle of the regular polygon = 150°.
For a regular polygon, the interior and exterior angles are supplementary: interior + exterior = 180°.
So the exterior angle \(= 180^\circ - 150^\circ = 30^\circ\).
The sum of all exterior angles of any polygon is 360°, and for a regular polygon each exterior angle \(= \dfrac{360^\circ}{n}\), where n is the number of sides.
Therefore \(n = \dfrac{360^\circ}{30^\circ} = 12\).
Hence the polygonal clock has 12 sides.
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