### Теория:

If a transversal line meets two lines, eight angles are formed at the points of intersection as shown in the Figure-1.

Figure-1

It is clear that the pairs of angles $$∠1, ∠2$$
, ; $$∠3, ∠4,$$ ; $$∠5, ∠6$$and $$∠7, ∠8$$ are linear pairs.

Besides, the pairs $$∠1, ∠3$$ ; $$∠2, ∠4$$ ; $$∠5, ∠7$$and $$∠6, ∠8$$ are vertically opposite angles.

We can further classify the angles into different categories as follows:

Corresponding angles:

Figure-2

Observe that the pair of angles $$∠1$$ and $$∠5$$ that are marked at the right side of the transversal line $$l$$. In that $$∠1$$ lies above the line $$m$$ and $$∠5$$ lies above the line $$n$$.

Also observe the pair of angles $$∠2$$ and $$∠6$$that are marked on the left of the transversal line $$l$$. In that $$∠2$$lies above $$m$$ and $$∠6$$lies above $$n$$.

In the same way observe the pair of angles $$∠3$$
and $$∠7$$ that are marked on left of transversal line $$l$$. In that $$∠3$$ lies below $$m$$ and $$∠7$$ lies below $$n$$.

Observe the pair of angles $$∠4$$
and $$∠8$$ that are marked on the right of transversal line $$l$$. In that $$∠4$$lies below $$m$$ and $$∠8$$ lies below $$n$$.

So all these pairs of angles have different vertices, lie on the same side (left or right) of the transversal line ($$l$$) lie above or below the lines $$m$$
and $$n$$. Such pairs are called corresponding angles.

Alternate Interior angles

Figure-3

Each of pair of angles named $$∠3$$ and $$∠5$$, $$∠4$$ and $$∠6$$ are marked on the opposite side of the transversal line $$l$$ and are lying between lines $$m$$ and $$n$$ are called alternate interior angles.

Alternate Exterior angles

Figure-4

Each pair of angles named $$∠1$$ and $$∠7$$, $$∠2$$ and $$∠8$$ are marked on the opposite side of the transversal line $$l$$ and are lying outside of the lines $$m$$ and $$n$$ are called alternate exterior angles.

Some more pairs of angles.

Figure-5

> Each pair of angles named $$∠3$$
and $$∠6$$, $$∠4$$ and $$∠5$$ are marked on the same side of transversal line $$l$$ and are lying between the lines $$m$$ and $$n$$. These angles are lying on the interior of the lines $$m$$ and $$n$$ as well as the same side of the transversal line $$l$$. Called as co-interior angles.

Figure-6

> Each pair of angles named $$∠1$$ and $$∠8$$, $$∠2$$ and $$∠7$$are marked on the same side of transversal line $$l$$ and are lying outside of the lines $$m$$ and $$n$$. These angles are lying on the exterior of the lines $$m$$ and $$n$$ as well as the same side of the transversal line $$l$$. Called as co-exterior angles.