Question

Can a triangle have more than one obtuse angle?

Answer 1

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+\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+\varepsilon`
`beta = 90+delta`

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

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