One of the angles with parallel lines and secant is 80 degrees. Find the rest of the angles.

Let line A parallel to B, and C – secant. Angle ∠1 = 80.

Angle ∠2 adjacent to angle ∠1. The sum of adjacent angles is 180, then ∠2 = (180 – 80) = 100.

The angle ∠5 = ∠1 = 80, ∠6 = ∠2 = 100 as the corresponding angles at the intersection of parallel lines A and B secant C.

The angle 3 = ∠5 = 63, ∠4 = ∠6 = 100, as the angles lying crosswise at the intersection of the secant C parallel to A and B.

The angle ∠7 = ∠7 = 80, like the vertical angles at the intersection of two straight lines.

Answer: ∠1 = ∠3 = ∠5 = ∠7 = 80, angle ∠2 = ∠4 = ∠6 = ∠8 = 100.