Examine whether you can construct $∆DEF$ such that $EF = 7.2\ cm$, $m\angle E = 110^{\circ}$ and $m\angle F = 80^{\circ}$. Justify your answer.

Given: $EF = 7.2\ cm$, $m\angle E = 110^{\circ}$ and $m\angle F = 80^{\circ}$.

To do: To examine whether $∆DEF$ can be constructed.

Solution: 

We know the angle sum property of a triangle which states that the sum of all angles in a triangle is always $180^{\circ}$.

So, $\angle E + \angle F + \angle D = 180^{\circ}$

$\Rightarrow 110^{\circ} + 80^{\circ} + \angle D = 180^{\circ}$

$\Rightarrow \angle D = -10^{\circ}$

Here we obtain a negative value for $\angle D$. So $\triangle DEF$ can't be constructed.