A K Upadhyay and S Upadhyay Solutions for Chapter: Lines and Angles, Exercise 2: EXERCISE 6.2

In the figure, $\mathrm{A}\mathrm{B}\parallel \mathrm{C}\mathrm{D}$ and $\mathrm{E}\mathrm{F}\parallel \mathrm{D}\mathrm{N}$. If $\mathrm{\angle }\mathrm{C}\mathrm{D}\mathrm{M}=35°$ and $\mathrm{\angle }\mathrm{B}\mathrm{E}\mathrm{F}=\mathrm{}65°$ then, find $\mathrm{\angle }\mathrm{M}\mathrm{D}\mathrm{N}, \mathrm{\angle }\mathrm{A}\mathrm{E}\mathrm{D}$ and $\mathrm{\angle }\mathrm{D}\mathrm{E}\mathrm{F}$.

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

In the figure, $\mathrm{P}\mathrm{Q}$ and $\mathrm{R}\mathrm{S}$ are two plane mirrors placed parallel to each other. An incident ray $\mathrm{A}\mathrm{B}$ strikes the mirror $\mathrm{P}\mathrm{Q}$ at $\mathrm{B}$, the reflected ray moves along the path $\mathrm{B}\mathrm{C}$ and strikes, mirror $\mathrm{R}\mathrm{S}$ at $\mathrm{C}$ and again reflects back along $\mathrm{C}\mathrm{D}$. Prove that $\mathrm{A}\mathrm{B}\mathrm{}\left|\right|\mathrm{}\mathrm{C}\mathrm{D}$.

In the figure, $\mathrm{P}\mathrm{Q}$ and $\mathrm{Q}\mathrm{R}$ are two plane mirrors placed perpendicular to each other. An incident ray $\mathrm{A}\mathrm{B}$ strikes the mirror $\mathrm{P}\mathrm{Q}$ at $\mathrm{B}$ and reflected towards $\mathrm{B}\mathrm{C}$. The reflected ray $\mathrm{B}\mathrm{C}$ strikes the mirror $\mathrm{Q}\mathrm{R}$ at $\mathrm{C}$ and reflected towards $\mathrm{CD}$. Prove that $\mathrm{A}\mathrm{B}\mathrm{}\left|\right|\mathrm{}\mathrm{C}\mathrm{D}$.

If the bisectors of a pair of corresponding angles formed by a transversal with two given lines are parallel, prove that the given lines are parallel.

In the figure, $AB\parallel CD$. Prove that $p+q+r={360}^o$

In the figure, $BA\parallel DE$. Prove that $\angle x-\angle y=\angle z$.

In the figure, line $l\parallel m.$ Find $x, y$ and $z$.