NCERT Solutions

In Fig. 6.13, lines AB and CD intersect at O . If $\angle \mathrm{AOC}+\angle \mathrm{BOE}=70^{\circ}$ and $\angle \mathrm{BOD}=40^{\circ}$, find $\angle \mathrm{BOE}$ and reflex $\angle \mathrm{COE}$.

In Fig. 6.14, lines XY and MN intersect at O . If $\angle \mathrm{POY}=90^{\circ}$ and $a: b=2: 3$, find $c$.

In Fig. 6.15, $\angle \mathrm{PQR}=\angle \mathrm{PRQ}$, then prove that $\angle \mathrm{PQS}=\angle \mathrm{PRT}$.

In Fig. 6.16, if $x+y=w+z$, then prove that AOB is a line.

In Fig. 6.17, POQ is a line. Ray OR is perpendicular to line PQ . OS is another ray lying between rays OP and OR. Prove that $\angle \mathrm{ROS}=\frac{1}{2}(\angle \mathrm{QOS}-\angle \mathrm{POS})$.

It is given that $\angle \mathrm{XYZ}=64^{\circ}$ and XY is produced to point P . Draw a figure from the given information. If ray YQ bisects $\angle \mathrm{ZYP}$, find $\angle \mathrm{XYQ}$ and reflex $\angle \mathrm{QYP}$.

In Fig. 6.23, if $\mathrm{AB}\|\mathrm{CD}, \mathrm{CD}\|\mathrm{EF}$ and $y: z=3: 7$, find $x$.

In Fig. 6.24, if $\mathrm{AB} \| \mathrm{CD}, \mathrm{EF} \perp \mathrm{CD}$ and $\angle \mathrm{GED}=126^{\circ}$, find $\angle \mathrm{AGE}, \angle \mathrm{GEF}$ and $\angle \mathrm{FGE}$.

In Fig. 6.25, if $\mathrm{PQ} \| \mathrm{ST}, \angle \mathrm{PQR}=110^{\circ}$ and $\angle \mathrm{RST}=130^{\circ}$, find $\angle \mathrm{QRS}$. [Hint : Draw a line parallel to ST through point R.]

In Fig. 6.26, if $\mathrm{AB} \| \mathrm{CD}, \angle \mathrm{APQ}=50^{\circ}$ and $\angle \mathrm{PRD}=127^{\circ}$, find $x$ and $y$.

In Fig. 6.27, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD . Prove that $\mathrm{AB} \| \mathrm{CD}$.