Question

The ratios of measures of the angles in Triangle ABC is 4:13:19. Find the measures of each of the angles. Show all of the work/explain.

Answer 1

`20^(\circ),\\ \\65^(\circ),\\ \\95^(\circ).`

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

`4x+13x+19x=180^(\circ),\\ \\36x=180^(\circ),\\ \\x=5^(\circ).`

Therefore, the angles of the triangle are

`4x=4\cdot 5=20^(\circ),\\ \\13x=13\cdot 5=65^(\circ),\\ \\19x=19\cdot 5=95^(\circ).`