Question

Two lines AB and CD intersect at O. If ∠AOC = 50°, find ∠AOD, ∠BOD and ∠BOC.

Answer 1

We know that if two lines intersect then the vertically-opposite angles are equal.
Therefore, $\angle AOC=\angle BOD=50°$
Let $\angle AOD=\angle BOC=x°$
Also, we know that the sum of all angles around a point is $360°$.
Therefore,
$$\begin{gathered} \angle AOC+\angle AOD+\angle BOD+\angle BOC=360° \\ \Rightarrow 50+x+50+x=360° \\ \Rightarrow 2x=260° \\ \Rightarrow x=130° \end{gathered}$$
Hence, $\angle AOD=\angle BOC=130°$
Therefore, $\angle AOD=130°,\angle BOD=50°\text{and}\angle BOC=130°$.