what is the value of $d$?

Explanation:

Step1: Sum adjacent angles on straight line

The angles on one side of a straight line add up to $180^\circ$. So first calculate the sum of the given angles: $30^\circ + 40^\circ = 70^\circ$

Step2: Find supplementary angle to $d$

Subtract the sum from $180^\circ$ to get the angle supplementary to $d$: $180^\circ - 70^\circ = 110^\circ$

Step3: Use vertical angles property

Vertical angles are equal, so $d$ equals the supplementary angle found: $d = 110^\circ$

Answer:

$110^\circ$