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A pair of parallel lines is cut by a transversal.

A pair of parallel lines is shown cut by a transversal. Angle A is located in the upper left exterior next to the transversal, and angle B is located in the bottom right exterior corner of the transversal.

If m∠A = (5x − 4)° and m∠B = (8x − 28)°, what is the value of x?

8
9.4
16.3
36

1 answer

To find the value of \( x \), we can use the property that angles formed by a transversal cutting parallel lines are either equal or supplementary. In this case, angles \( A \) and \( B \) are corresponding angles, which means they are equal.

Given: \[ m∠A = (5x - 4)° \] \[ m∠B = (8x - 28)° \]

Set the two expressions equal to each other: \[ 5x - 4 = 8x - 28 \]

Now, solve for \( x \).

  1. Subtract \( 5x \) from both sides: \[ -4 = 3x - 28 \]

  2. Add \( 28 \) to both sides: \[ 24 = 3x \]

  3. Divide both sides by \( 3 \): \[ x = 8 \]

Thus, the value of \( x \) is 8.