The angle $x^{\circ }$ and the angle below line $m$ and to the left of line $k$ are alternate interior angles.

The angle $a^{\circ }$ and the angle above line $m$ and to the right of line $k$ are corresponding angles.

The angle $x^{\circ }$ and the angle above line $m$ and to the left of line $k$ are corresponding angles.

The angle $a^{\circ }$ and the angle below line $m$ and to the left of line $k$ are alternate exterior angles.