Question

Which is not possible for triangle PQR and why?

$\angle P=30°,\angle Q=60°,\angle R=90°.$

Answer 1

Given: $$\begin{gathered} \angle P={30}^{\circ }, \\ \angle Q={60}^{\circ }and \\ \angle R={90}^{\circ } \end{gathered}$$

We know that, sum of all angles of triangle is 180°

$$\begin{gathered} \angle P+\angle Q+\angle R={180}^{\circ } \\ {30}^{\circ }+{60}^{\circ }+{90}^{\circ }={180}^{\circ } \\ So,yesthistriangleispossiblebecausethesumofalltheanglesis{180}^{\circ } \end{gathered}$$

Hence, the given angles form a triangle.