Question

Examine whether you can construct $\Delta DEF$ such that $EF=7.2cm,m\angle E=110°andm\angle F=80°$. Justify your answer.

Answer 1

Check whether angle sum property of triangle satisfy or not

It is given that

$$\begin{gathered} EF=7.2cm \\ \angle E=110° \\ \angle F=80° \end{gathered}$$

To check whether it is possible to construct $\Delta DEF$from the given values.

$\begin{array}{rcl}\angle E+\angle F& =& 110°+80°\\ & =& {190}^{\circ }\end{array}$

We observe that the sum of two angles is ${190}^{\circ }$ is greater that ${180}^{\circ }$

So, the angle sum property of triangle is not satisfied.

Thus, it is not possible to construct a triangle.