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In the given diagram, identify the parallel lines and angles and use the property of alternate interior angles to solve for x.

Mathematics

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  1. Identify parallel lines and angles.

    The diagram shows two parallel lines, indicated by the arrows. Let's call the top parallel line L1L_1 and the bottom parallel line L2L_2. So, L1∥L2L_1 \parallel L_2.
    Let the vertices of the triangle be AA (the top vertex, where the angle is 4x4x), BB (the bottom-left vertex), and CC (the bottom-right vertex).

  2. Use the property of alternate interior angles.

    Consider the line segment ABAB as a transversal intersecting the parallel lines L1L_1 and L2L_2.
    The angle 3x3x shown at the top-left is formed by $L_

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