Question

Line $m$ is parallel to line $n$ and line $p$ is parallel to line $q$ then the value of $x+y$ is

• A. ${180}^o$
• B. ${130}^o$
• C. ${230}^o$
• D. None of the above

Answer 1

The correct option is A ${180}^o$

we know,
$y={65}^o(\because \text{corresponding angles})$

Let corresponding angle of $x$ and supplementry angle of $y$ be $z$


$x=z(\because \text{corresponding angles})$
Also,
$z={180}^o-y(\because \text{linear pair})z={180}^o-{65}^{o}z={115}^o\because x=z\Rightarrow x={115}^o$
Now, $x+y={115}^o+{65}^o$
$x+y={180}^o$

ALTERNATE METHOD$:-
Irrespective of the angle given as ${65}^o$, we can solve this.
As $x=z(\because \text{Corresponding angles})$
and we know,
$y+z={180}^o(\because \text{Linear Pair})$
put $z=x$ in above equation, we get
$x+y={180}^o$