1. **State the problem:** We are given two expressions for angles: $m<7 = 15x - 1$ and $m<8 = 8x - 3$. We need to find the measures of angles 1, 2, and 3. 2. **Analyze the diagram and relationships:** Lines $r$ and $s$ are vertical and parallel, and line $q$ intersects them, creating eight angles. Angles 7 and 8 are adjacent at line $r$, so they form a linear pair and their measures sum to 180 degrees. 3. **Set up the equation for angles 7 and 8:** $$m<7 + m<8 = 180$$ Substitute the expressions: $$15x - 1 + 8x - 3 = 180$$ 4. **Simplify the equation:** $$23x - 4 = 180$$ 5. **Solve for $x$:** $$23x = 180 + 4$$ $$23x = 184$$ $$x = \frac{184}{23}$$ $$x = 8$$ 6. **Find $m<7$ and $m<8$ using $x=8$:** $$m<7 = 15(8) - 1 = 120 - 1 = 119$$ $$m<8 = 8(8) - 3 = 64 - 3 = 61$$ 7. **Find $m<1$ and $m<2$:** Angles 1 and 2 are vertical angles to angles 7 and 8 respectively, so they are equal: $$m<1 = m<7 = 119$$ $$m<2 = m<8 = 61$$ 8. **Find $m<3$:** Angles 3 and 7 are corresponding angles (since $r$ and $s$ are parallel and $q$ is a transversal), so: $$m<3 = m<7 = 119$$ **Final answers:** $$m<1 = 119$$ $$m<2 = 61$$ $$m<3 = 119$$