1. **State the problem:** We have a quadrilateral with angles labeled as $x^\circ$, $2x^\circ$, $130^\circ$, and $65^\circ$. We need to find the value of $x$. 2. **Formula and rules:** The sum of interior angles in any quadrilateral is $360^\circ$. So, we use the formula: $$x + 2x + 130 + 65 = 360$$ 3. **Set up the equation:** $$3x + 195 = 360$$ 4. **Solve for $x$:** Subtract 195 from both sides: $$3x + \cancel{195} - \cancel{195} = 360 - 195$$ $$3x = 165$$ Divide both sides by 3: $$\frac{3x}{\cancel{3}} = \frac{165}{\cancel{3}}$$ $$x = 55$$ 5. **Answer:** The value of $x$ is $55^\circ$.