Question

Solve the following:

a] The three angles of a triangle are in the ratio 2:3:5. Find the measure of each angle. Classify the triangle.

Answer 1

$$\begin{gathered} \mathrm{Let}\angle \mathrm{A}=2x;\angle \mathrm{B}=3x;\angle \mathrm{C}=5x \\ \mathrm{Now}, \\ \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180°\left[\mathrm{Angle}\mathrm{sum}\mathrm{property}\right] \\ \Rightarrow 2x+3x+5x\mathit{}=180° \\ \Rightarrow 10x=180° \\ \Rightarrow x=18 \\ \mathrm{Now},\angle \mathrm{A}=36°;\angle \mathrm{B}=54°;\angle \mathrm{C}=90° \end{gathered}$$

The given triangle is right angled triangle.