Question

Can two obtuse angles be supplementary?

Answer 1

Let $\angle \mathrm{A}$ and $\angle \mathrm{B}$ are obtuse angles

Supplementary angles are those angles that sum up to ${180}^0$.

$\Rightarrow \angle \mathrm{A}+\angle \mathrm{B}={180}^0$

$$\begin{gathered} If\angle \mathrm{A}>{90}^0 \\ \angle \mathrm{B}>{90}^0 \\ \Rightarrow \angle \mathrm{A}+\angle \mathrm{B}>{180}^0\ne {180}^0 \end{gathered}$$

Hence, no, two obtuse angles cannot be supplementary.