Two lines intersect, forming vertical angles measuring 3x + 10 and 5x - 20. What is the value of x?

Vertical angles are congruent, so set the expressions equal: $3x+10=5x-20$. Subtract $3x$ and add $20$: $30=2x$, so $x=15$, choice D. Check: both angles measure $3(15)+10=55$ and $5(15)-20=55$. Choice A ($5$) gives $25$ and $5$. Choice B ($35$) gives $115$ and $155$. Choice C ($25$) gives $85$ and $105$. Only $x=15$ makes the two angles equal. Note that adjacent angles, not vertical angles, would be supplementary. Checking the angle measures is quick and catches algebra slips.