In the picture, the two lines are blue, and the transversal is orange. Alternate angles lie between the two lines, but on either side of the transversal. The picture shows two pairs of alternate angles, one marked by red arrows, and the other marked by green arrows. Can you see how they are the angles inside a "z"-shape? The "z"-shape for the red angles runs along the top blue line from left to right up to the transversal, down the transversal and then from left to right along the bottom blue line. The "z"-shape for the green arrows is back-to-front: from right to left across the top line, down the transversal and from right to left along the bottom blue line.

In the picture, the two blue lines are parallel, so the transversal forms equal alternate angles. Both alternate angles marked in green are equal to \(60^\circ\). They are the angles inside a "z".

In the picture, the two blue lines are parallel, so the transversal forms equal alternate angles. Both alternate angles marked in green are equal to \(120^\circ\). They are the angles inside a back-to-front "z".

In the picture, the two blue lines are parallel, so the transversal forms equal alternate angles. The angles marked in pink are alternate angles, so they must be equal, and \(x\) must equal \(30^\circ\).