1. **State the problem:** We are given two angles formed by intersecting lines, labeled as $(2a+3)^\circ$ and $(6a+1)^\circ$. We need to find the value of $a$. 2. **Identify the relationship:** Since the two angles are formed by intersecting lines and are adjacent, they are supplementary angles. Supplementary angles add up to $180^\circ$. 3. **Write the equation:** $$ (2a+3) + (6a+1) = 180 $$ 4. **Simplify the equation:** $$ 2a + 3 + 6a + 1 = 180 $$ $$ 8a + 4 = 180 $$ 5. **Isolate the variable term:** $$ 8a + \cancel{4} - \cancel{4} = 180 - 4 $$ $$ 8a = 176 $$ 6. **Solve for $a$:** $$ \frac{8a}{\cancel{8}} = \frac{176}{\cancel{8}} $$ $$ a = 22 $$ 7. **Conclusion:** The value of $a$ is $22$ degrees.