Question

8TH GRADE MATH

Answer 1

Answer: choice G)

Corresponding angles are congruent; therefore, 2x+52 = 76

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Explanation:

Let's go through the answer choices one by one

• We can rule out choice F because 4x and 104 are alternate exterior angles. They are equal because line a and line b are parallel. So 4x = 104 is a valid equation to solve for x.
• Choice G is the answer because 2x+52 and 76 are not corresponding angles. One possible pair of corresponding angles are 2x+52 and 104. These two angles are in the southeast corner of each 4 corner angle configuration, which is why they correspond to one another. The pairing 2x+52 and 76 are instead supplementary, so those two angles add to 180.
• We can rule out choice H because 4x and 2x+52 are congruent vertical angles. Vertical angles form when we have an X shape from the intersection of two lines. Specifically vertical angles are opposite one another like the diagram shows.
• We can rule out choice J because the angles (4x) and (x+50) are supplementary. This means they add to 180. This applies to any pair of same side exterior angles. They are on the same side of the transversal line t. They are exterior because they are outside of the parallel lines a and b.