# How many obtuse angles does a triangle have?

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#### Explanation

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Nov 26, 2015

A triangle can have a maximum of $1$ obtuse angle.

#### Explanation:

Any triangle must have interior angles that add up to ${180}^{\circ}$. An obtuse angle is an angle greater than ${90}^{\circ}$ but less than ${180}^{\circ}$.

If you had an angle that was ${91}^{\circ}$. The other $2$ angles would have to be acute. This is because the other angles would take up ${180}^{\circ} - {91}^{\circ} = {89}^{\circ}$ of the triangle. Since ${89}^{\circ}$ is less than ${90}^{\circ}$, this means the other $2$ angles must both be acute. You are left with $1$ obtuse angle.

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