The variable and angles of each triangle are, respectively:
Case 15: x = 20. 40º, 60º, 80º.
Case 16: x = 30. 90º, 30º, 60º.
Case 17: x = 4.25. 37º, 83.25º, 59.75º.
How to determine the variable behind the angles of a triangle
In this question we need to determine the values of a variable x behind each of the three triangles. By Euclidean geometry we know that sum of internal angles always equals 180º. Then, we proceed to find the value of the variable for each case:
Case 15:
2 · x + 3 · x + 4 · x = 180º
9 · x = 180º
x = 20
The angles are 40º, 60º and 80º.
Case 16:
90º + x + 2 · x = 180º
3 · x = 90º
x = 30
The angles are 90º, 30º and 60º.
Case 17:
37º + (5 · x + 62º) + (3 · x + 47º) = 180º
8 · x + 109º = 143º
8 · x = 34º
x = 4.25
The angles are 37º, 83.25º and 59.75º.