Given data:
The first angle is ∠A=4x.
The second angle is ∠B=13x.
The third angle is ∠C=19x.
The expression for the angle sum property is,
∠A+∠B+∠C=180degrees.
Substitute the given values in the above expression.
4x+13x+19x=180
36x=180
x=5
Substitute 5 for x in the first angle.
∠A=4(5)
=20 degrees.
Substitute 5 for x in the second angle.
∠B=13(5)
=65 degrees.
Substitute 5 for x in the third angle.
∠A=19(5)
=95 degrees.
Thus, the first angle is 20 degrees, the second angle is 65 degrees, and the third angle is 95 degrees.