# Can an acute isosceles triangle have 2 angles that measure 40 degrees?

May 31, 2018

$\textcolor{b l u e}{\text{No}}$

#### Explanation:

By definition an acute triangle's angles are all less the ${90}^{\circ}$

Since the sum of all the angles is ${180}^{\circ}$, we have:

${40}^{\circ} + {40}^{\circ} + {\theta}^{\circ} = {180}^{\circ}$

${\theta}^{\circ} = {100}^{\circ}$.

So the third angle is greater than ${90}^{\circ}$. This means the triangle is obtuse, not acute.