Question

In triangle $PQR$, an exterior angle at $A$ measures ${160}^o$, and $\angle$ $Q={70}^o$. Which is the longest side of the triangle?

• A. $\overline{PR}$
• B. $\overline{PA}$
• C. $\overline{PQ}$
• D. $\overline{QR}$

Answer 1

The correct option is D $\overline{QR}$

By using exterior angle property,

$\angle P+\angle Q=\angle A$

$\Rightarrow \angle P+{70}^o={160}^o$

$\Rightarrow \angle P={160}^o-{70}^o$

$\Rightarrow \angle P={90}^o$

According to the triangle inequality theorem, the side that is opposite to the largest angle is largest.
So, in a right angle triangle, ${90}^o$ is the longest angle in any, $\overline{QR}$ is the side opposite to it.

Therefore, $\overline{QR}$ is the largest side.