Question

If $△PQR$ is right angled at $Q$, then .

• A. $\angle P<90°;\angle R<90°$
• B. $\angle P>90°;\angle R<90°$
• C. $\angle P>90°;\angle R>90°$

Answer 1

The correct option is A $\angle P<90°;\angle R<90°$

Let's draw a $△PQR$, right angled at $Q$$\Rightarrow \angle Q={90}^{\circ }$.
Now, according to the angle sum property of a triangle.
$\angle P+\angle Q+\angle R={180}^{\circ }$
$\Rightarrow \angle P+{90}^{\circ }+\angle R={180}^{\circ }$
$\Rightarrow \angle P+\angle R={90}^{\circ }$.
$\therefore$ If $△PQR$ is right angled at $Q$
$\Rightarrow \angle P+\angle R={90}^{\circ }$.
which is possible only if both $\angle P,\angle R<{90}^{\circ }$
$\therefore \angle P<{90}^{\circ };\angle R<{90}^{\circ }$.