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It is given that ABCD is a parallelogram with angles named in consecutive order, <1, <2, <3, and <4.

Opposite angles of a parallelogram are congruent. Thus
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and
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by the
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.

The sum of the interior angles of any quadrilateral is 360 degrees, so m<1+m<2+m<3+m<4 = 360 degrees.

Using the
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,
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Therefore, 2(m<1+m<2) = 360 degrees.

By the
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,
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Therefore, Angle 1 and Angle 2 are supplementary.