Looking at the diagram, the unknown angle and angle 155 degrees are linear pairs. They lie on a straight line. The sum of the angles(linear pairs) is 180 degrees. Let U represent the unknown angle. It means that
155 + U = 180
U = 180 - 155
U = 25 degrees
Also, the sum of the angles in a triangle is 180 degrees. This means that
25 + 9x + 7 + 3x + 4 = 180
Collecting like terms, it becomes
25 + 7 + 4 + 9x + 3x = 180
36 + 12x = 180
12x = 180 - 36
12x = 144
x = 144/12
x = 12
