Complete each statement by writing $<,=,or>$.

a. $m\angle 1\underset{¯}{?}m\angle 3$.

b. $m\angle 2\underset{¯}{?}m\angle 3$.

c. $m\angle 1\underset{¯}{?}m\angle 2$.

Pair of opposite angles formed by intersecting lines.

Name the points of line segments in the given figure

Since the lines AB and CD are intersecting lines therefore the angles 1 and 3 are vertically opposite angles. Hence both the angles are equal.

Therefore, the answer is.

As from the figure, the angles 2 and 4 are on the same side of the intersecting lines and angle 3 is the whole angle so $\angle 2+\angle 4=\angle 3$

If $a=b+c$ and $c>0$ then $a>c$. As $\angle 2+\angle 4=\angle 3$and $4>0$so $\angle 3>\angle 2$. It can be written as $\angle 2<\angle 3$.

Thus, the answer is $<$.

When two lines are intersecting lines then the opposite angles are equal in measure. Therefore, the angles 1 and 3 are equal angles.

As from the figure, $\angle 2+\angle 4=\angle 3$. From part (a) $\angle 1=\angle 3$. Therefore, $\angle 2+\angle 4=\angle 1$.

If $a=b+c$ and $c>0$ then $a>c$. As $\angle 2+\angle 4=\angle 1$and$4>0$so $\angle 1>\angle 2$.

Thus, the answer is $>$.