Part A

Which solution for the value of x in the figure is incorrect?

2x = x + 75
x = 75

2x + x + 75 = 180
3x + 75 = 180
3x = 105
x = 35

(1 point)

Solution A is incorrect.Solution B is incorrect.Both solutions are incorrect.Neither solution is incorrect.

Part B
Which reason could you give to explain your answer to the previous item?
(1 point)

The labeled angles are corresponding angles, which are congruent. Congruent angles have equal measures, so x + 75 should be set equal to 2x, not added to 2x and set equal to 180.The labeled angles are alternate interior angles, which are congruent. Congruent angles have equal measures, so x + 75 should be set equal to 2x, not added to 2x and set equal to 180.The labeled angles are same-side interior angles, which are supplementary. The measures of supplementary angles total 180 degrees, so x + 75 plus 2x should be set equal to 180. The angle measures should not be set equal to each other.The labeled angles are a linear pair, which mean that they are supplementary. The measures of supplementary angles total 180 degrees, so x + 75 plus 2x should be set equal to 180. The angle measures should not be set equal to each other.

welll, the angles should be supplemeentary since they are a linear pair, so the correct answer shoudl be something nlike

2x+x+75=180
3x+75=180
x+25=60
x=35

so the answers are
A. solution B is incorrrect
B. the 2nd to last option (they are a same-side interior angle, which mean that they are supplemtnary... The angle measures should not be set equal to each other)

Answer Link

MsEHolt MsEHolt · Answer 2 · 2025-03-26T12:07:33-04:00

The correct answers are:

Part A: Solution A is incorrect.

Part B: The labeled angles are same-side interior angles, which are supplementary. The measures of supplementary angles total 180 degrees, so x + 75 plus 2x should be set equal to 180.

Explanation:

The two angles listed are same-side interior angles. This is because they are inside the block of parallel lines and on the same side of the transversal (the side of the trapezoid). Same-side interior angles are supplementary, so these angles must be supplementary. This means their sum is 180°:

2x+x+75 = 180