Question

Lines x and y are parallel.

Given the diagram, 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 can form a straight line which measures 180°.
D) (7x – 2)° + m∠2 = 106° because the sum of the remote interior angles equals the exterior angle.

Answer 1

Option C.

Explanation:

Option A. The given lines x and y are parallel and line s is a transverse.

Therefore, ∠1 and angle (6x + 8°) will be equal as they are corresponding internal angles. Option A is true.

Option B. ∠1 + 106° = 180° ( supplementary angles )

∠1 = 180 - 106 = 74° Option B is also true

Option C. x and y are parallel lines and t is the transverse.

Therefore, angle between ( 6x + 8)° and (7x - 2)° will be equal to ∠2.

∠2 + (6x + 8)° + (7x - 2)° = 180° [ angles at a point on a straight line]

But in this option ∠1 is given in place of ∠2.

Option C is incorrect.

Option D. ∠1 + ∠2 + (7x - 2)° = 180° [sum of all angles in a triangle measure 180°]

(7x - 2)° + ∠2 = 180 - ∠1

(7x - 2)° + ∠2 = 180° - 74°

(7x - 2) + ∠2 = 106°

This option is also correct.

Option C. is the answer.