Question

Can two obtuse angles be adjacent?

Answer 1

Acute Angle :
Acute angle is one which is more than 90° and less than 180°.

Two angles are said to be adjacent when they share :
--> Common arm 
--> Common vertex.

Yes, Two acute angles can be adjacent angles .

Proof:
example : Consider two adjacent figure ∠AOB and ∠AOC 
 given in the attachment.
∠AOB and ∠AOC share
-->common arm OB and
--->common vertex O.
hence ∠AOB and ∠AoC are acute as well as adjacent angles.

Answer 2

yes
hope it helps
if helps than say thanks