Answer:
[tex]20^{\circ},\\ \\65^{\circ},\\ \\95^{\circ}.[/tex]
Step-by-step explanation:
If the ratio of measures of the angles in the triangle ABC is 4:13:19, then angles of this triangles have measures 4x, 13x and 19x.
The sum of the measures of all interior angles of the triangle is always equal to 180°, then
[tex]4x+13x+19x=180^{\circ},\\ \\36x=180^{\circ},\\ \\x=5^{\circ}.[/tex]
Therefore, the angles of the triangle are
[tex]4x=4\cdot 5=20^{\circ},\\ \\13x=13\cdot 5=65^{\circ},\\ \\19x=19\cdot 5=95^{\circ}.[/tex]
