Suppose two adjacent angles are supplementary. Show that if one of them is an obtuse angle, then the other angle must be acute.

As we know, in case of supplementary angles the sum of angles must be 180°

Let two adjacent angles are x and y.

For these angles to be supplement,

x + y = 180° …(1)

let x = 120° (obtuse angle)

put it in (1)

120° + y = 180°

⇒ y = 180° - 120°

y = 60° (i.e. acute angle)

hence, to have a pair of supplementary angle if one angle is obtuse then other must be acute angle.