We want to know the measures of the angles of a triangle, given that the ratio of them is 8:3:4. Also, the sum of the angles must be 180°.
As their ratio is 8:3:4, we have that the angles of the triangles should be 8x, 3x and 4x (where x represents just a part of the división of the angles). Thus:
[tex]8x+3x+4x=180^{\circ}[/tex]
Solving for x, we obtain:
[tex]\begin{gathered} 15x=180^{\circ} \\ x=\frac{180^{\circ}}{15}=12^{\circ} \end{gathered}[/tex]
And thus, the angles will be:
[tex]\begin{gathered} 8x=8(12^{\circ})=96^{\circ} \\ 3x=3(12^{\circ})=36^{\circ} \\ 4x=4(12^{\circ})=48^{\circ}_{} \end{gathered}[/tex]
This means that the angles of the triangle should be: 96°, 36° and 48°. We verify that those are the angles of a triangle as:
[tex]96^{\circ}+36^{\circ}+48^{\circ^{}}=180^{\circ}[/tex]
