1. **State the problem:** Solve the equation $$\frac{(N-2)180}{N} = 150$$ for $N$. 2. **Understand the formula:** This equation often appears in polygon interior angle problems, where $N$ is the number of sides, and the formula $$\frac{(N-2)180}{N}$$ gives the measure of each interior angle in degrees. 3. **Multiply both sides by $N$ to eliminate the denominator:** $$ (N-2)180 = 150N $$ 4. **Distribute 180:** $$ 180N - 360 = 150N $$ 5. **Bring all terms involving $N$ to one side:** $$ 180N - 150N = 360 $$ 6. **Simplify:** $$ 30N = 360 $$ 7. **Divide both sides by 30:** $$ N = \frac{360}{30} = 12 $$ **Final answer:** $N = 12$