Question

find the number of sides of a polygon if each interior angle is 150​

Answer 1

Its interior angle has measure 150∘150∘. Therefore, the exterior angle has measure 180∘−150∘=30∘180∘−150∘=30∘.

Regular polygons have the property that the sum of all its exterior angles is 360∘360∘. Using this property, we can see that

number of sides= 12

Note: The sum of the interior angles of this regular polygon will be 150∘×12=1800∘150∘×12=1800∘. It is useful to know the relation between the interior angles, the exterior angles and the number of sides of a regular polygon. There is a formula to find the sum of interior angles of a polygon using the number of sides. This formula uses the fact that we can divide a regular polygon into triangles.

Step-by-step explanation:

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