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Two parallel lines are intersected by two transversals. The arrows on the lines indicate that they are parallel. Find the value of x.

Mathematics

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Let's find the value of xx.

The image shows two parallel lines intersected by two transversals. The arrows on the lines indicate that they are parallel. We will use the property of consecutive exterior angles.

  1. Analyze the angles on the left transversal.

    The angle xx (top-left exterior) and the angle 5x5x (bottom-left exterior) are consecutive exterior angles. When two parallel lines are cut by a transversal, the sum of consecutive exterior angles on the same side of the transversal is 180∘180^\circ.
    So, we can write the equation:

    x+5x=180∘x + 5x = 180^\circ

  2. Solve for xx using the left transversal.

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