Answer
$\angle(2)=55^{\circ}$
$\angle(3)=125^{\circ}$
$\angle(4)=55^{\circ}$
Work Step by Step
For $\angle(2)$, you need to know that $\angle(1)$ and $\angle(2)$ form a straight line, so they are $supplementary$, meaning they add up to $180^{\circ}$.
$\angle(1)+\angle(2)=180^{\circ}$
$125^{\circ}+\angle(2)=180^{\circ}$
$\angle(2)=180^{\circ}-125^{\circ}=55^{\circ}$
$\angle(3)$ is opposite $\angle(1)$ meaning they are equal. I will prove this in a bit.
$\angle(4)$ is also $supplementary$ to $\angle(1)$ so it should have the same angle measurement as $\angle(2)$.
$\angle(2)$ and $\angle(4)$ are opposite, and they are equal. This is because $180^{\circ}-\angle(x)$ would give the $supplementary$ angle and $180^{\circ}-(180^{\circ}-\angle(x))$=$\angle(x)$. Therefore $\angle(3)=125^{\circ}$.
