Problem
GEO-B1-M01-P002 Angles Formed by Intersecting Lines
#2
★☆☆☆☆ Level 1 of 5
Lines \(AB\) and \(CD\) intersect at \(O\). It is known that \(\angle AOC=64^\circ\). Find \(\angle BOD\), \(\angle AOD\), and \(\angle BOC\).
Vertical angles are equal, and adjacent angles sum to \(180^\circ\).
Angles \(AOC\) and \(BOD\) are vertical, so \(\angle BOD=64^\circ\). Angle \(AOD\) is adjacent to \(AOC\), hence \(\angle AOD=180^\circ-64^\circ=116^\circ\). Angle \(BOC\) is vertical to \(AOD\), so \(\angle BOC=116^\circ\).
Useful as an oral warm-up before parallel lines.