Question

Can two angles be supplementary, if both of them be obtuse.

Answer 1

Hint: Obtuse angle is an angle that is greater than ${90^\circ }.$

Complete Step by step solution:
Let $x$ and $y$ are two obtuse angles.
Since obtuse angle is greater than ${90^\circ }$. We get,
$4x > {90^\circ }$and $\angle y > {90^\circ }$
Adding the two of them, we get
$\angle x + \angle y > {90^\circ } + {90^\circ }$
$\angle x + \angle y > 180^\circ $ . . . . . (1)
Now, let us assume that angles $x$ and $y$ are also supplementary angles. Then their sum is equal to${180^\circ }$
$\angle x + \angle y = {180^\circ }$ . . . . . . (2)
But this cannot be true.
As equation (1) shows that $\angle x + \angle y$ is greater than$180^\circ $
There, $\angle x$ and $\angle y$cannot be supplementary if both of them are obtuse angles.

Note: - The method of proof used above is called proof by contradiction. In this method, first we assume that the result is true, and then prove that our assumption was wrong. It is a very effective method for solving questions like this one.