Question

Can two angles be supplementary if both of them are obtuse?

Answer 1

Supplementary angles:

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

Supplementary angles are those angles that sum up to $180°$.

i.e $\angle \mathrm{A}+\angle \mathrm{B}={180}^{\circ }$

If $\angle \mathrm{A}>{90}^{\circ }$ and $\angle \mathrm{B}>{90}^{\circ }$,

Then

$\begin{array}{rcl}\angle \mathrm{A}+\angle \mathrm{B}& >& {90}^{\circ }+{90}^{\circ }\\ \angle \mathrm{A}+\angle \mathrm{B}& >& {180}^{\circ }\end{array}$

$\begin{array}{rcl}& \ne & {180}^{\circ }\end{array}$

Example:

Let $\angle \mathrm{A}=91°$ and $\angle \mathrm{B}=91°$ which are obtuse angles, then

$\begin{array}{rcl}\angle \mathrm{A}+\angle \mathrm{B}& =& 91°+91°\\ & =& 182°\\ & \ne & 180°\end{array}$

Hence, no two angles are supplementary if both of them are obtuse