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

Measures of the angles are 20°, 65° and 95°.

Explanation:

We are given that,

Ratio of the angles of the triangle ABC is 4 : 13 : 19.

Let the constant corresponding to the measures of the angle = x.

So, the measures of the angles will be,

`4x, 13x, 19x`

Since, the sum of measures of the angles of a triangle is 180°.

We get,

`4x+13x+19x=180`

i.e.
`36x=180`

i.e. x = 5

Thus, the measures of the angles are,

4x = 4×5 = 20°

13x = 13×5 = 65°

19x = 19×5 = 95°

Also, sum of the obtained measures = 20° + 65° + 95° = 180°.

Hence, the measures of the angles are 20°, 65° and 95°.