# Can a triangle have more than one obtuse angle?

Jun 21, 2018

No.

#### Explanation:

The sum of all the inner angles of a triangle must be exactly $180$ degrees.

An obtuse angle is more than $90$ degrees, say $90 + \setminus \varepsilon$, meaning "something more than $90$.

Now assume that a triangle has angles $\alpha$, $\beta$ and $\gamma$. Assume that $\alpha$ and $\beta$ (for example) are obtuse. This means that they both have that "something more" than $90$ degrees. Say for example

$\alpha = 90 + \setminus \varepsilon$
$\beta = 90 + \delta$

This means that $\alpha + \beta = 90 + \setminus \varepsilon + 90 + \delta = 180 + \varepsilon + \delta$

So, $\alpha$ and $\beta$ alone are already more than $180$, and we didn't even add $\gamma$ yet!