From a point $O$ in a line $AB,$ ray $OC$ and $OD$ are drawn on opposite sides of $AB$ such that $\angle BOC=\angle AOD$. Prove that $OC$ and $OD$ are opposite rays.

In the given figure, $AB\parallel CD, \angle BPR=130°$ and $\angle CQR=30°$. Find $\angle PRQ$.

In the given figure, $l\parallel m$ and transversal $n$ intersects $l$ and $m$ at $A$ and $B$ respectively. If $\angle 1:\angle 2=3:2$. Determine all the eight angles.

In the given figure, $AB\parallel \parallel DE$. Find $x$.