1. **Problem statement:** Given two adjacent angles on a straight line, where the left angle is $4d^\circ + 16^\circ$ and the right angle is $2d^\circ + 14^\circ$, find the value of $d$. 2. **Formula and rule:** Angles on a straight line sum to $180^\circ$. So, $$ (4d + 16) + (2d + 14) = 180 $$ 3. **Set up the equation:** $$ 4d + 16 + 2d + 14 = 180 $$ 4. **Combine like terms:** $$ 6d + 30 = 180 $$ 5. **Isolate $d$:** $$ 6d = 180 - 30 $$ $$ 6d = 150 $$ 6. **Divide both sides by 6:** $$ \cancel{6}d = \frac{150}{\cancel{6}} $$ $$ d = 25 $$ 7. **Final answer:** $$ d = 25 $$ This means the value of $d$ that satisfies the angle relationship on the straight line is 25 degrees.