You're given one angle and asked for another. Don't reach for a protractor — the position of the two angles already tells you the answer.
The Two Moves
One — name the pair. Look at where the known angle and the wanted angle sit, and trace the shape between them. An F means corresponding. A Z means alternate. A C (or U) means co-interior. That single letter is the whole decision.
Two — apply its rule. F and Z are equal, so just copy the angle across. C is supplementary, so the wanted angle is 180° − the known one.
A Worked One
Two parallel lines, a transversal, and the angle 62° is marked. The wanted angle x sits in the same corner at the other crossing — that's an F, corresponding. Corresponding angles are equal, so x = 62°. Done in one line of working: "x = 62° (corresponding angles, parallel lines)".
When It's Co-interior
If the two angles trace a C, they're co-interior and they don't match — they add to 180°. Given 115°, the partner is 180 − 115 = 65°. Same two moves: name the pair (C), then apply its rule (subtract from 180).