A K Upadhyay and S Upadhyay Solutions for Chapter: Lines and Angles, Exercise 5: TEST YOURSELF

In the given figure, if $\mathrm{\angle }\mathrm{C}\mathrm{O}\mathrm{A}={62}^{\mathrm{o}}$, then $x$ is:

In the given Figure, if $\mathrm{\angle }\mathrm{A}\mathrm{B}\mathrm{D}={106}^{\mathrm{o}}$ and $\mathrm{\angle }\mathrm{A}\mathrm{C}\mathrm{F}={118}^{\mathrm{o}},\mathrm{}$then value of $\mathrm{\angle }\mathrm{A}$ is

In Figure, if $\mathrm{P}\mathrm{Q}\perp \mathrm{P}\mathrm{S}$. $\mathrm{P}\mathrm{Q}\parallel \mathrm{S}\mathrm{R}$. $\angle SQR=28°$ and $\mathrm{\angle }\mathrm{Q}\mathrm{R}\mathrm{T}=65°,$ then find the values of $x$ and $y$.

In the figure, $BD\parallel CE,$ find $x,y$ and $z.$

In figure, the side $\mathrm{Q}\mathrm{R}\mathrm{}$of $∆\mathrm{P}\mathrm{Q}\mathrm{R}$ is produced to a point $\mathrm{S}.$ If the bisector of $\mathrm{\angle }\mathrm{P}\mathrm{Q}\mathrm{R}$ and $\mathrm{\angle }\mathrm{P}\mathrm{R}\mathrm{S}$ meet at point T, then prove that $\mathrm{\angle }\mathrm{Q}\mathrm{T}\mathrm{R}=\frac{1}{2}\mathrm{\angle }\mathrm{Q}\mathrm{P}\mathrm{R}.$

Prove that the sum of the angles of triangle is ${180}^{\mathrm{o}}$

If two parallel lines are intersected by a transversal then prove that the bisectors of any pairs of alternate interior angles are parallel.

In $∆ABC$, $OB$ and $OC$ are bisectors of $\angle EBC$ and $\angle FCB$ which meet at point $O$. Prove that $\angle BOC=90°-\frac{1}{2}\angle BAC.$