the measure of each interior angle of a regular polygon is 150°. find the number of sides.\nnumber of sides =

Explanation:

Step1: Recall interior angle formula

For a regular polygon with ( n ) sides, the measure of each interior angle ( I ) is given by ( I=\frac{(n - 2)\times180^{\circ}}{n} ). We know ( I = 150^{\circ} ), so we set up the equation ( 150=\frac{(n - 2)\times180}{n} ).

Step2: Solve the equation

Multiply both sides by ( n ): ( 150n=(n - 2)\times180 ).
Expand the right - hand side: ( 150n = 180n-360 ).
Subtract ( 150n ) from both sides: ( 0 = 30n-360 ).
Add 360 to both sides: ( 30n = 360 ).
Divide both sides by 30: ( n=\frac{360}{30}=12 ).

Answer:

12