Question

Identify the segments that are parallel, if any, if ∠DCB and ∠CDA are supplementary.

Answer 1

Answer:

C

Step-by-step explanation:

We are given that

$\angle$DCB and $\angle$CDA are supplementary.

We have to identify the parallel segments if $\angle$DCB and $\angle$CDA are supplementary.

Supplementary angles: If the angles are supplementary then the sum of two angles is 180 degrees.

Therefore,

$\angle DCB+\angle CDA=180^{\circ}$

Therefore, angle DCB and angle CDA are interior angles .

Because CA is a transversal line and sum of interior angles is 180 degrees.

When the sum of interior angles formed between two lines  and on same side of transversal line is 180  degrees. Then the lines are parallel.

Therefore, angle DCB and angle CDA are formed between line AD and BC.

Hence, AD is parallel to BC.

Option C is correct.