Question

In $△DEF$, the exterior angle at D measures ${150}^{\circ }$ and $\angle E$ measures ${80}^{\circ }$. Which of the following options show the correct relation?

• A. DF $>$ DE
• B. DE $<$ EF
• C. DF $<$ DE
• D. DF $<$ EF

Answer 1

The correct option is A DF $>$ DE

In $△DEF$,
$\angle EDF={180}^{\circ }$ – ${150}^{\circ }={30}^{\circ }$ [Linear pair]
and, $\angle$EFD = ${180}^{\circ }$ - ${80}^{\circ }$ - ${30}^{\circ }$ = ${70}^{\circ }$ [Angle sum property of a triangle]
We know that in any triangle, the side opposite to the larger angle is longer.
Hence, DF $>$ DE $>$ EF.
Hence the answer.