Lines x and y are parallel. Which statement is not true? A) m∠1 = (6x + 8)° because they are corresponding angles. B) m∠1 = 74° because ∠1 is supplementary to the angle marked 106°. C) m∠1 + (6x + 8)° + (7x – 2)° = 180° because they form a straight line, which measures 180°. D) (7x – 2)° + m∠2 = 106° because the sum of the remote interior angles is equal to the exterior angle.

To identify which statement is not true, we need to consider the properties of parallel lines and the angles formed when they are intersected by a transversal.

A) If lines x and y are parallel and m∠1 is a corresponding angle to an angle on line y, then m∠1 should equal (6x + 8)° by the Corresponding Angles Postulate. This statement could be true given that the lines are parallel.

B) If m∠1 is supplementary to an angle marked 106°, then they should add up to 180° because supplementary angles have a sum of 180°. Therefore, m∠1 = 180° - 106° = 74°. This statement is true.

C) If m∠1, (6x + 8)°, and (7x – 2)° form a straight line, their measures should indeed add up to 180° due to the Straight Angle Theorem. This statement could be true as long as these angles are consecutive along a straight line.

D) This statement indicates that (7x – 2)° and m∠2 are remote interior angles to an exterior angle of 106°. However, the sum of the remote interior angles equals the exterior angle only in the context of a triangle. Since we have not been given any information that suggests that these angles are part of a triangle, statement D is likely the one that is not true, as it inaccurately applies a property of triangles to a situation that does not seem to involve a triangle.

Therefore, the statement that is not true based on the information provided is:

D) (7x – 2)° + m∠2 = 106° because the sum of the remote interior angles is equal to the exterior angle.