In the diagram with parallel lines AB and CD intersected by a transversal, and with angle <3 measuring 120°, the corresponding angles theorem establishes that angle <6 shares an equal measure of 120°.
In the provided diagram, two parallel lines, AB and CD, are intersected by a transversal. Given that the measure of angle <3 is 120°, we aim to determine the measure of angle <6.
The corresponding angles theorem states that when two parallel lines are cut by a transversal, corresponding angles are congruent. Corresponding angles occupy the same relative position with respect to the parallel lines and the transversal. In the given figure, angles 3 and 6 are corresponding angles since they are both situated in the interior of quadrilateral ABCD and on the same side of the transversal.
As per the corresponding angles theorem, we conclude that the measure of angle <6 is equal to the measure of angle <3. Given that m<3 is specified as 120°, it follows that m<6 = m<3 = 120°.