91Ó°ÊÓ

$m∠1=135°$. The figure is shown below.

• When two lines intersect, the angles opposite each other are called ‘vertical angles’ and they have the same measure.
• If two adjacent angles form a straight angle, then the two angles are supplementary angles and the sum of their measures is$180°$.

In the given figure, $∠1$and $∠3$ are vertical angles. So, they should have the same measure. Therefore,

$m∠3=m∠1=135°$

Also, in the given figure, $∠1$ and $∠2$ are supplementary angles as they are adjacent and form a straight angle. So, the sum of their measures should be $180°$.

Therefore,

$\begin{array}{c}m∠1+m∠2=180°\\ m∠2=180°−m∠1\\ =180°−135°\\ =45°\end{array}$

Similarly, $∠1$ and $∠4$ are supplementary angles.

Therefore,

$\begin{array}{c}m∠1+m∠4=180°\\ m∠4=180°−m∠1\\ =180°−135°\\ =45°\end{array}$