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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