In the adjoining figure, lines $AB$ and $CD$ are parallel. Find the values of $x$ and $y$.

 

All linear pairs are supplementary angles whereas all supplementary angles are not linear pairs.

Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle? Justify your answer.

In the adjoining figure, $OQ$ bisects $\angle AOB$. $OP$ is a ray opposite to ray $OQ$. Prove that $\angle POA=\angle POB$.

In figure given below, ray $OC$ stands on line $AB$ and $4x-3y=20$. Find the measures of $\angle BOC$ and $\angle AOC$.

In figure given below, lines $AB$ and $CD$ intersect each other at the point $O$. If $\angle AOC=45°$, find the values of $x,y \text{and} z$.

In figure given below, $l\parallel m$ and $n\parallel p$. If $\angle 1=60°$, then prove that $\angle 2=2\angle 1$.

In the figure given below, $AF\parallel BD$ and $AF$ is a bisector of $\angle EAC$. If $\angle EAC=70°$, find the measure of $\angle ABC$ and $\angle ACD$. 

In the figure given below, $AB\parallel CD$. If $\angle EAB=50°$ and $\angle ECD=100°$, find $\angle AEC$.