Question

In triangle PQR if $\angle P=30°,\angle Q=2\angle R$, find the measures of ∠Q and ∠R.

Answer 1

We have a triangle PQR:

We know that sum of all interior angles of a triangle is 180°

Given angles: $\angle P=30°,\angle Q=2\angle R$

$$\begin{gathered} \Rightarrow \angle P+\angle Q+\angle R={180}^{\circ } \\ \Rightarrow {30}^{\circ }+2\angle R+\angle R={180}^{\circ } \\ \Rightarrow 3\angle R={180}^{\circ }-{30}^{\circ } \\ \Rightarrow \angle R=\frac{{150}^{\circ }}{3}={50}^{\circ } \\ \Rightarrow \angle R={50}^{\circ } \\ \Rightarrow \angle Q=2\times {50}^{\circ } \\ \Rightarrow \angle Q={100}^{\circ } \end{gathered}$$

Hence, the required angles are $\angle Q=100°and\angle R=50°$.