consecutive angles in a parallelogram
Check the final answer first, then review the worked steps.
Problem
consecutive angles in a parallelogram
Answer
D. supplementary
Step-by-step solution
- Definition of a parallelogram: A parallelogram is a quadrilateral where both pairs of opposite sides are parallel.
- Analyze the properties of angles: In a parallelogram, consecutive angles (angles that share a common side) are formed by two parallel lines intersected by a transversal (the side connecting them).
- Apply geometric theorems: According to the properties of parallel lines, interior angles on the same side of a transversal are supplementary, meaning their sum is $180^{\circ}$. Therefore, any two consecutive angles in a parallelogram add up to $180^{\circ}$.
- Conclusion: Since the sum of the two consecutive angles is $180^{\circ}$, they are defined as supplementary angles.