Solve (n-2)*180^circ/n*5=360

$$\frac { ( n - 2 ) \times 180 ^ { \circ } } { n } \times 5 = 360$$

Solve for n

$$n = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

Steps for Solving Linear Equation

Divide both sides by 5.

$$\frac{\left(n-2\right)\times 180}{n}=\frac{360}{5}$$

Divide 360 by 5 to get 72.

$$\frac{\left(n-2\right)\times 180}{n}=72$$

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n.

$$\left(n-2\right)\times 180=72n$$

Use the distributive property to multiply n-2 by 180.

$$180n-360=72n$$

Subtract 72n from both sides.

$$180n-360-72n=0$$

Combine 180n and -72n to get 108n.

$$108n-360=0$$

Add 360 to both sides. Anything plus zero gives itself.

$$108n=360$$

Divide both sides by 108.

$$n=\frac{360}{108}$$

Reduce the fraction \frac{360}{108} to lowest terms by extracting and canceling out 36.

$$n=\frac{10}{3}$$