In a set of three lines, a pair of parallel lines is intersected by a transversal. The intersection forms eight special angles. Two of the special angles, A andB, are corresponding angles. For the set of parallel lines intersected by a transversal, A=4x andB=-5(x-18). Part A: Write an equation to represent the corresponding relationship betweenA andB. Part B: Use the equation to find the measures ofA andB.

answer:

Use an equation to represent the corresponding angle relationship between A and B.

Ans:

4x = 2(x + 14)

Since they are corresponding, they are considered equal.

Use the equation to find the measures of A and B.

Ans: Solve for x and substitute it for the angles.

4x = 2(x + 14)

4x = 2x + 28

4x - 2x = 28

2x = 28

x = 28 ÷ 2

x = 14

Now substitute:

Remember, ∠A = ∠B

∠A = 4(14)

∠B = 2(14 + 14)

4(14) = 2(14 + 14)

56 = 2(28)

56 = 56

Correct

56° is the measure for angles for ∠A and ∠B

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