R Chandra Solutions for Chapter: Lines and Angles, Exercise 3: TEST YOUR SKILLS

In the figure $\mathrm{O}\mathrm{A}\mathrm{}\left|\right|\mathrm{}\mathrm{Q}\mathrm{P}\mathrm{}$ and $\mathrm{}\mathrm{O}\mathrm{B}\mathrm{}\left|\right|\mathrm{}\mathrm{Q}\mathrm{R}$, $\mathrm{\angle }\mathrm{A}\mathrm{O}\mathrm{B}+\mathrm{\angle }\mathrm{P}\mathrm{Q}\mathrm{R}$?

The difference between two complementary angles is $15°$, what are the measure of the angles?

In the figure, line $\mathrm{l}\left|\right|\mathrm{}\mathrm{m}\mathrm{}$and $\mathrm{}\mathrm{m}\left|\right|\mathrm{}\mathrm{n}$. If $\mathrm{p}\mathrm{}$and $\mathrm{}\mathrm{q}$ are transversal then what is the measure of $\mathrm{x}$?

The supplement of an angle is $\frac{1}{5}\mathrm{}$of it. Determine their difference.

The complementary angles are in the ratio $1:5$ Find their difference.

What value of $\mathrm{x}$ would make $\mathrm{P}\mathrm{O}\mathrm{Q}$ a straight line?

Let $\mathrm{OA}, \mathrm{OB},\mathrm{OC}$ and $\mathrm{OD}$ be rays in anticlockwise direction starting from $\mathrm{OA}$ such that $\angle \mathrm{AOB}=\angle \mathrm{COD}=100º, \angle \mathrm{BOC}=82º$ and $\angle \mathrm{AOD}=78º$. IS it true that $\mathrm{AOC}$ and $\mathrm{BOD}$ are straight lines? Justify your answer.

In the given figure, if $\mathrm{A}\mathrm{B}\mathrm{}\left|\right|\mathrm{}\mathrm{C}\mathrm{D},$ $\mathrm{\angle }\mathrm{A}\mathrm{P}\mathrm{Q}=60°$  and $\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{\angle }\mathrm{P}\mathrm{R}\mathrm{D}=137°$ then find $\mathrm{x}\mathrm{}$and $\mathrm{y}$.