In the adjoining figure, two plane mirrors $I$ and $II$ are placed parallel to each other. $AM$ and $BN$ are perpendiculars to the mirrors $I$ and $II$ respectively. If an incident ray strikes the mirror $I$ at $A$ and the reflected ray strikes the mirror$II$ at $B$, then the value of $x$ is

In the adjoining figure, two plane mirrors $I$ and $II$ are placed perpendicular to each other. $PM$ and $QN$ are perpendiculars to the mirrors $I$ and $II$ respectively. If an incident ray strikes the mirror $I$ at $P$ and the reflected ray strikes the mirror$II$ at $Q$, then the value of $x$ is

In the adjoining diagram, $DE\parallel BC$. Find the value of $x$.

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 $x,y \text{and} z$.