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the ratio of the numbers of sides of two polygons is 1:2. if each interior angle of the first polygon is 120degree, then the measure of each interior angle of the second polygon is​

User AlVaz
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Answer:

150°

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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User Mitomed
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