Question

In the figure above, lines $l$ and $m$ are parallel and lines $s$ and $t$ are parallel. If the measure of $\angle 1$ is ${35}^o$, what is the measure of $\angle 2$?

• A. ${35}^o$
• B. ${55}^o$
• C. ${70}^o$
• D. ${145}^o$

Answer 1

The correct option is D ${145}^o$

From the figure, we understand that $\angle 1$ and $\angle 3$ together form a straight line.
Thus, $\angle 1+\angle 3={180}^0$
$\Rightarrow {35}^0+\angle 3={180}^0$
$\Rightarrow \angle 3={145}^0$
Now, since $l$ and $m$ are parallel lines cut by transversals $s$ and $t$, $\angle 3$ an $\angle 4$ are corresponding angles.
We know that corresponding angles are equal. Thus $\angle 4=\angle 3={145}^0$
Similarly $\angle 2$ an $\angle 4$ are corresponding angles.
Thus $\angle 2=\angle 4={145}^0$