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?

a) Yes, we can have two obtuse angles whose sum is a reflex angle.

We know that,

Obtuse angle is one that measures between 90° and 180°.

Reflex angle is one that measures between 180° and 360°.

So, suppose we have two obtuse angles of measure 100° and 105° then their sum 205° lies between 180° and 360° and ∴ is a reflex angle.

You can think of more such examples.

b) No, we cannot have two obtuse angles whose sum is a complete angle.

We know that,

Complete angle measures 360° and obtuse angle is one that measures between 90° and 180°.

If we take two 180° angles then we can obtain a complete angle but 180° is not an obtuse angle. So, in any case we cannot obtain a complete angle using two obtuse angles.