Question

which sides of quadrilateral abcd must be parallel? explain.
m∠a = 52, m∠b = 33, m∠c = 147, m∠d = 128
the sides by the

Explanation:

Step1: Check consecutive - angle sums

We know that if two lines are cut by a transversal and the consecutive interior angles are supplementary (\(m\angle1 + m\angle2=180^{\circ}\)), then the two lines are parallel.
For sides \(AB\) and \(CD\) with transversal \(AD\): \(m\angle A+m\angle D = 52^{\circ}+128^{\circ}=180^{\circ}\)
For sides \(AB\) and \(CD\) with transversal \(BC\): \(m\angle B + m\angle C=33^{\circ}+147^{\circ}=180^{\circ}\)

Answer:

The sides \(AB\) and \(CD\) by the Consecutive - Interior Angles Converse.