1. **State the problem:** We are given that the measure of angle 2 is expressed as $m\angle 2 = 18 + 6x$ degrees, and another angle in the figure measures 132°. 2. **Identify the relationship:** Since the triangle has a right angle and two sides marked equal, the triangle is isosceles with the right angle, so the other two angles inside the triangle are equal. 3. **Calculate the other angles inside the triangle:** The sum of angles in a triangle is 180°. One angle is 90° (right angle), and one angle is 132° outside the triangle, so angle 2 is the exterior angle adjacent to one of the equal angles inside the triangle. 4. **Use the exterior angle theorem:** The exterior angle equals the sum of the two opposite interior angles. Here, $m\angle 2 = 132^\circ$. 5. **Set up the equation:** Given $m\angle 2 = 18 + 6x$ and $m\angle 2 = 132$, we have $$18 + 6x = 132$$ 6. **Solve for $x$:** $$6x = 132 - 18$$ $$6x = 114$$ $$x = \frac{114}{6}$$ $$x = 19$$ 7. **Final answer:** The value of $x$ is $19$.