Intersecting Lines & Angles

Let two lines intersect, forming four angles: $a, b, c$, and $d$. Suppose we are given that angle $a$ is $75^{\circ}$. Because angle $a$ and angle $b$ form a linear pair on a straight line, they must add up to $180^{\circ}$. We can calculate angle $b$ by subtracting $75^{\circ}$ from $180^{\circ}$, which gives us . Now, since angle $a$ and angle $c$ are vertically opposite angles, their measures must be . Therefore, angle $c$ also measures $75^{\circ}$. Finally, angle $b$ and angle $d$ are vertically opposite, so angle $d$ must measure .