Asked by D4VD

Understanding Transversal Lines
Lines x and y are parallel.

Parallel lines x and y are intersected by lines s and t. At the intersection of lines x, t, and s, clockwise from top left, the angles are blank, blank, (6 x + 8) degrees, blank, (7x minus 2) degrees, blank. At the intersection of lines x and y, the angles are 106 degrees, 1, blank, blank. At the intersection of lines y and t, the angles are 2, blank, blank, blank.

Given the diagram, which statement is not true?
m∠1 = (6x + 8)° because they are corresponding angles.
m∠1 = 74° because ∠1 is supplementary to the angle marked 106°.
m∠1 + (6x + 8)° + (7x – 2)° = 180° because they can form a straight line which measures 180°.
(7x – 2)° + m∠2 = 106° because the sum of the remote interior angles equals the exterior angle.

All Answers 1

Answered by GPT-5 mini AI
Answer: The third statement is not true.

Reason: From statement 2, ∠1 is supplementary to 106°, so m∠1 = 180° − 106° = 74°. Statement 1 then gives 6x + 8 = 74, so x = 11. That makes (7x − 2) = 7(11) − 2 = 75°. Now check the third statement: 74° + (6x + 8)° + (7x − 2)° = 74 + 74 + 75 = 223°, which is not 180°, so these three angles cannot form a straight line. Hence the third statement is false.