1. **State the problem:** We are given the angle measure equation for question 37: $$m\angle 2 = 5x - 8$$ and the angle measure is $$58^\circ$$. 2. **Set up the equation:** Since $$m\angle 2 = 58^\circ$$, we have: $$5x - 8 = 58$$ 3. **Solve for $$x$$:** Add 8 to both sides: $$5x - 8 + 8 = 58 + 8$$ $$5x = 66$$ Divide both sides by 5: $$\frac{\cancel{5}x}{\cancel{5}} = \frac{66}{5}$$ $$x = \frac{66}{5} = 13.2$$ 4. **Interpretation:** The value of $$x$$ that satisfies the angle measure equation is $$13.2$$. --- **Note:** The user asked to solve the other questions except 37, so we will solve question 34 next. --- **Question 34:** Given a right triangle with legs labeled $$x$$ and $$11$$, find the hypotenuse. 1. **State the problem:** Find the hypotenuse $$c$$ of a right triangle with legs $$x$$ and $$11$$. 2. **Formula:** Use the Pythagorean theorem: $$c = \sqrt{x^2 + 11^2}$$ 3. **Simplify:** $$c = \sqrt{x^2 + 121}$$ Since $$x$$ is unknown, this is the expression for the hypotenuse. --- **Question 35:** Given an equilateral triangle with sides $$6$$, $$6$$, and base $$-6 + 2x$$, find $$x$$. 1. **State the problem:** In an equilateral triangle, all sides are equal, so: $$6 = -6 + 2x$$ 2. **Solve for $$x$$:** Add 6 to both sides: $$6 + 6 = 2x$$ $$12 = 2x$$ Divide both sides by 2: $$\frac{\cancel{2}x}{\cancel{2}} = \frac{12}{2}$$ $$x = 6$$ --- **Question 36:** Given a triangle with sides $$7$$, $$x + 18$$, and an unlabeled side, insufficient information is provided to solve for $$x$$. --- **Question 38:** Already solved in the prompt: $$x = 9.5$$. --- **Question 39:** Given $$m\angle 2 = 7x - 2$$ and $$m\angle 2 = 62^\circ$$, solve for $$x$$. 1. **Set up the equation:** $$7x - 2 = 62$$ 2. **Solve for $$x$$:** Add 2 to both sides: $$7x = 64$$ Divide both sides by 7: $$\frac{\cancel{7}x}{\cancel{7}} = \frac{64}{7}$$ $$x = \frac{64}{7} \approx 9.14$$