R S Aggarwal Solutions for Chapter: Properties of Parallel Lines, Exercise 1: EXERCISE 14

In the adjoining figure, it is given that $AB\parallel CD$, $\angle ABO=50°$, $\angle CDO=40°$. Find the measure of $\angle BOD$.

In the given figure, $AB\parallel CD$ and a transversal $EF$ cuts them at $G$ and $H$ respectively.
If $GL$ and $HM$ are the bisectors of the alternate angles $\angle AGH$and $\angle GHD$ respectively, prove that $GL\parallel HM$.

In the given figure, $AB\parallel CD$, $\angle ABE=120°$, $\angle ECD=100°$, and $\angle BEC=x°$.
Find the value of $x$.

In the given figure, $ABCD$ is a quadrilateral in which $AB\parallel DC$ and $AD\parallel BC$.

Prove that $\angle ADC=\angle ABC$.

In the given figure, $l\parallel m$ and $p\parallel q$.
Find the measure of each of the angles $\angle a$, $\angle b$, $\angle c$ and $\angle d$.

In the given figure, $AB\parallel DC$ and $AD\parallel BC$, and $AC$ is a diagonal. If $\angle BAC=35°$,$\angle CAD=40°$, $\angle ACB=x°$, and $\angle ACD=y°$, find the value of $x$ and $y$.

In the given figure, $AB\parallel CD$ and $CA$ has been produced to $E$ so that $\angle BAE=125°$.
If$\angle BAC=x°$, $\angle ABD=x°$, $\angle BDC=y°$ and $\angle ACD=z°$, find the values of $x$, $y$, $z$.

In each of the given figures, two lines $l$ and $m$ are cut by a transversal $t$.
Find whether $l\parallel m$.