Question

In the adjoining figure line $p||$ line $q$. Line $‘t^{\prime }$ and line $‘s^{\prime }$ are transversals. Find the measure of $\angle x$ and $\angle y$ using the measures of angles given in the figure.

Answer 1

Given:
Line $p||$ line $q$, line $t$ and line $s$ are transversals.
Let us find the measure of $\angle x$ and $\angle y$.

Firstly, Let us consider $\angle z$ as shown in figure.
Measure of $\angle z=40°$ … (i) [Since, they are corresponding angles]
So,
$\angle x+\angle z=180°$ [Since, angles are in a linear pair]
$\angle x+40°=180°$ [From equation (i)]
$\angle x=180°-40°$
$\angle x=140°$
Now, let us consider $\angle w$ as shown in the figure.
$\angle w+70°=180°$ [Since, angles are in a linear pair]
$\angle w=180°-70°$
$\angle w=110°$ ... (ii)
It is given that, line $p||$ line $q$ and line ${}^{\prime }{s}^{\prime }$ is a transversal.
So, $\angle y=\angle w$ [by using alternate angles]
$\angle y=110°$ [From equation (ii)]
$\therefore$ The measure of $\angle x$ is $140°$ and $\angle y$ is $110°$.