Question

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

Answer 1

Given:

In $△DEF$,

$\angle E={110}^{\circ },\angle F={80}^{\circ },\angle EF=7.2\text{cm}$

Here, $\angle E+\angle F={110}^{\circ }+{80}^{\circ }={190}^{\circ }$

Which is not possible in any triangle.

Since,

Angle sum property of a triangle: In any triangle, sum of its interior angles is equal to ${180}^{\circ }$.

Hence, $\Delta DEF$ can not be constructed.