Question: Find the measure of each marked angle. Assume the lines are parallel.
$(x+5)^\circ$
$(9x-25)^\circ$
$x + 5 = \square^\circ$
$9x - 25 = \square^\circ$
(Simplify your answers. Type an integer or a fraction.)
1. **State the problem:** We need to find the measures of the two marked angles given by $(x+5)^\circ$ and $(9x-25)^\circ$ where the lines are parallel and cut by a transversal.
2. **Identify the relationship:** Since the lines are parallel, the two marked angles are corresponding angles and therefore equal.
3. **Set up the equation:**
$$x + 5 = 9x - 25$$
4. **Solve for $x$:**
$$x + 5 = 9x - 25$$
$$5 + 25 = 9x - x$$
$$30 = 8x$$
$$x = \frac{30}{8}$$
$$x = \frac{15}{4}$$
5. **Find each angle measure:**
- First angle:
$$x + 5 = \frac{15}{4} + 5 = \frac{15}{4} + \frac{20}{4} = \frac{35}{4} = 8.75^\circ$$
- Second angle:
$$9x - 25 = 9 \times \frac{15}{4} - 25 = \frac{135}{4} - 25 = \frac{135}{4} - \frac{100}{4} = \frac{35}{4} = 8.75^\circ$$
6. **Conclusion:** Both angles measure $\frac{35}{4}^\circ$ or $8.75^\circ$.
**Final answers:**
$$x + 5 = \frac{35}{4}^\circ$$
$$9x - 25 = \frac{35}{4}^\circ$$