In the given diagram, we have a pair of parallel lines intersected by a transversal line. 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 alternate interior to the angle (4x - 10)°.
Therefore, we can write: A = (4x - 10)°.
Angle B is corresponding to the angle (4x - 10)°.
Therefore, we can write: B = (4x - 10)°.
Angle C is alternate interior to the angle 2x°.
Therefore, we can write: C = 2x°.
Angle D is corresponding to the angle 2x°.
Therefore, we can write: D = 2x°.
Since the sum of angles in a straight line is 180°, we can set up the equation:
A + B + C + D = 180°
Substituting the known values, we get:
(4x - 10)° + (4x - 10)° + 2x° + 2x° = 180°
Simplifying the equation, we can solve for x:
8x - 20 + 4x + 4x = 180
16x - 20 = 180
16x = 200
x = 12.5
Therefore, the value of x is 12.5.
Please note that this solution assumes the given diagram accurately represents the angle relationships.