Lines AB and CD cross at O. $\angle AOC = (3x + 10)^\circ$ and $\angle BOD = (5x - 30)^\circ$. What is $\angle BOC$?

Explanation

1. 01

   $\angle AOC$ and $\angle BOD$ are vertically opposite, so they are equal: $3x + 10 = 5x - 30$, giving $x = 20$.

2. 02

   So $\angle AOC = 3 \times 20 + 10 = 70^\circ$.

3. 03

   $\angle BOC$ sits next to $\angle AOC$ on the straight line AB, so $\angle BOC = 180^\circ - 70^\circ = 110^\circ$.