Question

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?

Answer 1

a) Yes, the sum of two obtuse angles is always greater than ${180}^{\circ }$. Hence, the sum of two obtuse angles may be a reflex angle.

b) No, the sum of two obtuse angles cannot be ${360}^{\circ }$. Because each obtuse angle lies between ${90}^{\circ }$ and ${180}^{\circ }$. So, the sum of the two obtuse angles lies between ${180}^{\circ }$ to ${360}^{\circ }$ .