1. **State the problem:** We need to solve for the value of $q$ given two angles: $(q + 2)^\circ$ and $(3q - 2)^\circ$. 2. **Analyze the angles:** The problem suggests these two angles are adjacent and likely form a straight line (since one is vertical downward and the other diagonal upward-left), meaning their sum is $180^\circ$. 3. **Set up the equation:** $$ (q + 2) + (3q - 2) = 180 $$ 4. **Simplify the equation:** $$ q + 2 + 3q - 2 = 180 $$ $$ 4q = 180 $$ 5. **Solve for $q$:** $$ q = \frac{180}{4} $$ $$ q = 45 $$ 6. **Conclusion:** The value of $q$ is $45$ degrees. Note: The user mentioned $q=60$ but based on the angle sum, $q=45$ is the correct solution.