Question

Quadrilateral is a parallelogram.

1. Why is supplementary to ?
2. Why is supplementary to ?
3. Complete: consecutive angles of a parallelogram are ?, while opposite angles are?.

Short answer

1. is supplementary to because these are the adjacent angles on the same side of a transversal and therefore their sum is .
2. is supplementary to because these are the adjacent angles on the same side of a transversal and therefore their sum is.
3. Consecutive angles of a parallelogram are supplementary, while opposite angles are congruent.

Step-by-step solution

Step 1. Observe the diagram.

The given diagram is:

Step 2. Description of step.

It is being given that is a parallelogram.

Therefore, and

As, and is a transversal and the angles and are the adjacent angles on the same side of a transversal.

Therefore, the sum of the angles and is .

Therefore, is supplementary to .

Step 3. Description of step.

Therefore, is supplementary to because these are the adjacent angles on the same side of a transversal and therefore their sum is .

Step 1. Observe the diagram.

The given diagram is:

Step 2. Description of step.

It is being given that is a parallelogram.

Therefore, and .

As, and is a transversal and the angles and are the adjacent angles on the same side of a transversal.

Therefore, the sum of the angles and is .

Therefore, is supplementary to .

Step 3. Description of step.

Therefore, is supplementary to because these are the adjacent angles on the same side of a transversal and therefore their sum is .

Step 1. Observe the diagram.

The given diagram is:

Step 2. Description of step.

In the parallelogram the sum of the adjacent angles is and the opposite angles have the same measure.

Therefore, in parallelogram consecutive angles of a parallelogram are supplementary and opposite angles are congruent.

Step 3. Write the complete step.

Consecutive angles of a parallelogram are supplementary, while opposite angles are congruent.