Mathematics

Can we have two obtuse angles whose sum is(a) A reflex angle? Why or why not?(b) A complete angle? Why or why not?

SOLUTION
Let,
$A$  and $B$  be two obtuse angles.
Then by definition,
$90^\circ<A<180^\circ$  and
$90^\circ<B<180^\circ$

Adding the two equations, we get
$\therefore 90^\circ+90^\circ<A+B<180^\circ+180^\circ$
$\Rightarrow 180^\circ<A+B<360^\circ\qquad...(i)$

(a) From equation (i),
$180^\circ<A+B<360^\circ$
i.e., $A+B$ is an obtuse angle.

(b) From equation (i),
$A+B<360^\circ$
Hence, $A+B$ can not be a complete angle.

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Subjective Medium Published on 09th 09, 2020
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