R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: EXERCISE 7B

Two adjacent angles on a straight line are in the ratio$5:4$. Find the measure of each of these angles.

 If two straight lines intersect each other in such a way that one of the angles formed measure$90°$, show that each of the remaining angles measures $90°$.

Two lines$\mathrm{AB} \mathrm{and} \mathrm{CD}$ intersect at a point $\mathrm{O}$such that $\angle \mathrm{BOC}+\angle \mathrm{AOD}=280°$, as shown in the figure. Find all the four angles.

Two lines $AB$ and $CD$ intersect each other at a point $O$ such that $\angle \mathrm{AOC}:\angle \mathrm{AOD}=5:7$. Find all the angles.

In the given figure, three lines $AB, CD$ and $EF$ intersect at a point $O$ such that $\angle AOE=35°$ and $\angle BOD=40°$. Find the measure of $\angle AOC$, $\angle BOF$, $\angle COF$ and $\angle DOE$.

In the given figure, the two lines $AB$ and $CD$ intersect at a point $O$ such that $\angle BOC=125°.$ Find the values of $x, y \mathrm{and} z$.

If two straight lines intersect each other then prove that the ray opposite to the bisector of one of the angles so formed bisects the vertically opposite angle.

Prove that the bisectors of two adjacent supplementary angles include a right angle.