1. **State the problem:** Given $m<6 = 8x - 3$ and $m<7 = 15x - 1$, find the measures of angles 6 and 7. 2. **Identify the relationship between angles 6 and 7:** Since lines $r$ and $s$ are parallel and $q$ is a transversal, angles 6 and 7 are consecutive interior angles (same side interior angles), which are supplementary. 3. **Write the supplementary angle equation:** $$m<6 + m<7 = 180$$ 4. **Substitute the given expressions:** $$8x - 3 + 15x - 1 = 180$$ 5. **Combine like terms:** $$23x - 4 = 180$$ 6. **Solve for $x$:** $$23x = 180 + 4$$ $$23x = 184$$ $$x = \frac{184}{23}$$ $$x = 8$$ 7. **Find each angle measure:** $$m<6 = 8(8) - 3 = 64 - 3 = 61$$ $$m<7 = 15(8) - 1 = 120 - 1 = 119$$ 8. **Check the sum:** $$61 + 119 = 180$$ which confirms the solution. **Final answer:** $$m<6 = 61^\circ, \quad m<7 = 119^\circ$$