Two lines $l$ and $m$ are perpendicular to the same line $n$. Are $l$ and $m$ perpendicular to each other? Given reason for your answer.

In the given figure, $OD$ is the bisector of $\angle AOC, OE$ is the bisector of$\angle BOC$ and $OD\perp OE$. Show that the points $A,O$and $B$ are collinear.

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In the given figure, $\angle 1=60°$ and $\angle 6=120°$. Show that the lines m and n are parallel.

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$AP$ and $BQ$ are the bisectors of the two alternate interior angles formed by intersection of a transversal $t$ with the parallel lines $l$ and $m$. See the given figure. Show that $AP\parallel BQ.$

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If in the given figure, bisectors $AP$ and $BQ$of the alternate interior angles are parallel, then show that $l\parallel m$.

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In the given figure, $BA\parallel ED$ and $BC\parallel EF$. Show that $\angle ABC=\angle DEF.$

[Hint: Produce $DE$ to intersect $BC$at $P$ (say)].

In the given figure, $BA\parallel ED$and$BC\parallel EF$. Show that $\angle ABC+\angle DEF=180°.$

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In the given figure, $DE\parallel QR$ and$AP$and $BP$ are the bisectors of $\angle EAB$and $\angle RBA$, respectively. Find $\angle APB$.

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The angles of a triangle are in the ratio $2 : 3 : 4$. Find the angles of the triangle.