1. The problem states that the circle is divided into four sectors with angles 18°, $x$, $2x$, and 147°. 2. Since the total angle around a point in a circle is 360°, the sum of all sector angles must equal 360°. 3. Write the equation: $$18 + x + 2x + 147 = 360$$ 4. Combine like terms: $$18 + 147 + x + 2x = 360$$ $$165 + 3x = 360$$ 5. Subtract 165 from both sides: $$\cancel{165} + 3x - \cancel{165} = 360 - 165$$ $$3x = 195$$ 6. Divide both sides by 3: $$\frac{3x}{\cancel{3}} = \frac{195}{\cancel{3}}$$ $$x = 65$$ Final answer: $x = 65$ degrees.