Answer:
150°
Step-by-step explanation:
You want to know the measure of an interior angle of a regular polygon that has twice as many sides as one with an interior angle of 120°.
Exterior angle
The exterior angle of a regular polygon is the supplement of the interior angle. The polygon with an interior angle of 120° has an exterior angle of ...
180° -120° = 60°
The sum of exterior angles is 360°, so there must be 360°/60° = 6 of them. In the polygon with twice as many sides, there will be twice as many exterior angles, so each will measure 360°/12 = 30°.
Interior angle
The corresponding interior angle is ...
180° -30° = 150°
The measure of each interior angle of the second polygon is 150°.
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