Same formalism defining triangle type in terms of angles

Question

What same formalism can be used to define triangle type in terms of it's angles $\alpha,\beta,\gamma$ ? I can think just one :

Right triangle $$ \{\alpha,\beta+\gamma \} \ni k = \pi/2 $$

Bonus points - from this we can deduce, that : $$ \quad\sum_{k\in \{\alpha,\beta+\gamma \}}^n k = \alpha+\beta+\gamma = n \frac{\pi}{2} = \pi $$

Acute triangle

$$ \{\alpha,\beta, \gamma \} \ni k < \pi/2 $$

Obtuse triangle

$$ \{\alpha,\pi- \left(\beta+\gamma\right) \} \ni k > \pi/2 $$

Any other uniform ways to describe triangle type in terms of it's angles ?

Answer 1

Let $\alpha, \beta, \gamma$ be the angles of the triangle. Then the triangle is (acute, right, obtuse) when $\max(\alpha, \beta, \gamma)$ is ($<$, $=$, $>$) $\pi/2$.