Is it true that if two parallel lines are intersected by a secant, then the corresponding angles can be obtuse?

No, this statement is incorrect, since: a straight line forms an angle of 180 degrees. If we divide this angle by a straight line, in any case, we get at least two right angles (180-90 = 90) or one obtuse angle and one acute angle = (180 – A; either A is acute or another angle is acute – according to the properties of an obtuse angle ( degree value from 90 to 180)).