Question

Can two obtuse angles form a linear pair?

Answer 1

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

Linear pairs of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other and sum of them $={180}^0$.

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

But

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

Hence, no, two obtuse angles cannot form a linear pair.