Question

given: ( overline{ab} parallel overline{dc} ) and ( mangle2 = mangle4 ) prove: ( overline{ad} parallel overline{bc} ) what is the missing statement in the proof? ( mangle1 = mangle4 ) ( mangle1 + mangle4 = 180^{circ} ) ( mangle2 + mangle3 = 180^{circ} )

Explanation:

Step1: Recall the definition of supplementary angles

If two angles are supplements, then the sum of their measures is \(180^{\circ}\).
Since \(\angle1\) and \(\angle4\) are supplements (from statement 3), by the definition of supplementary angles, \(m\angle1 + m\angle4=180^{\circ}\)

Answer:

\(m\angle1 + m\angle4 = 180^{\circ}\)