Question

In the adjoining figure. line $p||$ line $q$. line $l||$ line $m$. Find measures of $\angle a,\angle b$, and $\angle c$, using the measures of given angles. Justify your answers.

Answer 1

Given:
Line $p||$ line $q$ and line $l$ are transversal.
Line $l||$ line $m$ and line $p$ is a transversal.
Line $p||$ line $q$ and line $m$ is a transversal.
Firstly let us find the measure of $\angle a$
Line $p||$ line $q$ and line $l$ are transversal.
So,
$\angle a+80°=180°$ [Since, they are interior angles]
$\angle a=180°–80°$
$\angle a=100°$
Now, line $l||$ line $m$ and line $p$ is a transversal.
So, $\angle c=80°$ … (i) [By using exterior alternate angles]
Line $p||$ line $q$ and line $m$ is a transversal.
So, $\angle b=\angle c$ … [Since, they are corresponding angles]
$\angle b=80°$ … [From equation (i)]
$\therefore$ The measure of $\angle a$ is $100°,\angle b$ is $80°,\angle c$ is $80°$.