In the given diagram, we have two parallel lines intersected by a transversal. To determine the relationship between the angles and solve for x, we can use the properties of angles formed by parallel lines and a transversal.
From the diagram, we can observe the following angle relationships:
Angle A is corresponding to the angle (4x - 3)°.
Therefore, we can write: A = (4x - 3)°.
Angle B is alternate interior to the angle (7x + 9)°.
Therefore, we can write: B = (7x + 9)°.
Angle C is alternate interior to the angle 2x°.
Therefore, we can write: C = 2x°.
Since the sum of angles in a straight line is 180°, we can set up the equation:
A + B + C = 180°
Substituting the known values, we get:
(4x - 3)° + (7x + 9)° + 2x° = 180°
Simplifying the equation, we can solve for x:
4x - 3 + 7x + 9 + 2x = 180
13x + 6 = 180
13x = 174
x = 13.38
Therefore, the value of x is approximately 13.38.
Please note that this solution assumes the given diagram accurately represents the angle relationships.