Ratio of Angles in a Triangle

Let the angles be $3 \alpha, 4\alpha, 5\alpha$ . Since the angles in a triangle sum up to $180^\circ$ , we have $12 \alpha = 180^\circ$ $\Rightarrow \alpha = 15^\circ$ . Thus, the largest angle is $5 \times 15^\circ = 75^\circ$ .

Note: The angles are in a $3:4:5$ ratio does not imply that the sides are in a $3:4:5$ ratio. The latter gives a right-angled triangle.

The angles are: $\textcolor{#3D99F6}{3x}, \textcolor{#D61F06}{4x}, \textcolor{#20A900}{5x}$

$\\ \begin{aligned} \text{Sum of angles} &= \textcolor{#3D99F6}{3x} + \textcolor{#D61F06}{4x} + \textcolor{#20A900}{5x} \\ 180 &= \textcolor{#3D99F6}{3x} + \textcolor{#D61F06}{4x} + \textcolor{#20A900}{5x} \\ 180&= 12x \\ 15 &= x \end{aligned}$

$\begin{aligned} \text{Largest angle} &= 5x \\ &= 5(15) \\ &= \boxed{75} \end{aligned}$

since the angles of a triangle is 180, 3x+4x+5x=180,12x=180,x=15 largest angle =5x=5x15=75