Question

Angle 'p' of a triangle is 1/3 of angle R and angle Q is less than angle R by 1/3rd of it. Find the angles of the triangle.

Answer 1

Dear student
$$\begin{gathered} Let\hspace{0.17em}\angle Rbex \\ Then,A.T.Q \\ \angle P=\frac{1}{3}x \\ \angle Q=x-\frac{1}{3}x \\ Nowbyanglesumpropertyof△ \\ \angle P+\angle Q+\angle R=180° \\ \Rightarrow \frac{1}{3}x+x-\frac{1}{3}x+x=180° \\ \Rightarrow 2x=180° \\ \Rightarrow x=90°=\angle R \\ So\angle \mathrm{P}=30° \\ \angle Q=90°-\frac{1}{3}\times 90° \\ \Rightarrow \angle Q=90°-30°=60° \end{gathered}$$
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