Question

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

Answer 1

Given $\angle ABD$ and $\angle DBC$ are supplementary angles.

$\angle ABD$ is obtuse angle

We have to prove that if one is obtuse, the other is acute angle.

$\angle ABD+\angle DBC={180}^o$

$\angle DBC={180}^o-\angle ABD$

$\Rightarrow \angle ABD>{90}^o$

$\therefore \angle DBC<{180}^o-{90}^o={90}^o$

$\Rightarrow \angle DBC$ is an acute angle