Question

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 and B, are corresponding angles.

For the set of parallel lines intersected by a transversal, A=4x and B=-5(x-18).

Part A: Write an equation to represent the corresponding relationship betweenA andB.
Part B: Use the equation to find the measures of A and B.

Answer 1

Part A: 4x = -5(x-18)

Part B: A and B both = 40 degrees

Corresponding angles, found at the same position on two parallel lines intersected by a transversal, have equal measures. Therefore, if the upper right angle on one line is denoted as A, it will be equal to the upper right angle on the other line, denoted as B.

Starting with the given equation: 4x = -5(x - 18)

Expand the equation: 4x = -5x + 90

Isolate the variable x: 9x = 90

Solve for x: x = 10

Now, calculate the angles:

Angle A = 4x = 4 * 10 = 40 degrees

Since angle B is also the upper right angle on the other parallel line, it will have the same measure: Angle B = 40 degrees.

Explanation:

Hope this helps

Answer 2

Part A: 4x = -5(x-18)

Part B: A and B both = 40 degrees

Explanation:

Ok, corresponding angles are in the same position on the two parallel lines cut by the transversal. And they are equal in measure. So, upper right = upper right.

So A = B

4x = -5(x -18)

4x = -5x + 90

9x = 90

x = 10

Angle A = 4x = 40 degrees, which means angle B is also 40, but let's show the work:

Angle B = -5(x - 18) = -50 + 90 = 40