Question 180206
No.
The sum of the 3 angles of a triangle equals 180.
1.{{{A+B+C=180}}}
If two angles (A,B) are greater than 90, then their sum would be greater than 180.
{{{A+B=180+DELTA}}}
where {{{DELTA}}} is some arbitrarily small positive amount.
Then substituting into eq. 1,
 1.{{{A+B+C=180}}}
{{{180+DELTA+C=180}}}
{{{DELTA+C=0}}}
{{{C=-DELTA}}}
We've shown that the remaining angle (C) would need to be negative to make the sum equal 180.
That's not possible, therefore two obtuse angles would not be allowed in a triangle.