Exercise

In the figure, $AB$ is parallel to $CD$. If the measure of $\angle x$ is $k°$, then find the value of $k$.

In the figure, $AB$ is parallel to $CD$. If the measure of $\angle x$ is $k°$, then find the value of $k$.

In the figure, $AB$ is parallel to $CD$. If the measure of $x$ is $k°$, the find the value of $k$.

Consider the given pair of triangles and say whether they are congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:

$△ABC$ and $△DEF$ are two triangles in which $AB=DF, \angle ACB=70°, \angle ABC=60°; \angle DEF=70°$ and $\angle EDF=60°$. Prove that the triangles are congruent.

Find all the three angles of the $△ABC$.

In a parallelogram $ABCD$, the bisectors of the consecutive angles $\angle A$ and $\angle B$ insersect at $P$. Show that $\angle APB={90}^{\circ }$

If $PQRS$ is a cyclic quadrilateral in which $\angle PSR={70}^{\circ }$ and $\angle QPR={40}^{\circ }$, then find $\angle PRQ$ (see Fig. 4.81).