Question

what is the name of the pair of angles ∠dbe and ∠ebc whose noncommon sides are opposite rays that form a straight line? options: vertical angles, complementary angles, linear pair, adjacent angles

Explanation:

1. Recall the definitions:

• Vertical angles: Opposite angles formed by intersecting lines, not relevant here.
• Complementary angles: Sum to \(90^\circ\), not defined by forming a straight line.
• Linear pair: Adjacent angles whose non - common sides are opposite rays and form a straight line (sum to \(180^\circ\)).
• Adjacent angles: Share a common side and vertex, but not all adjacent angles form a straight line.

1. For \(\angle DBE\) and \(\angle EBC\), they share a common side \(BE\), have the same vertex \(B\), and their non - common sides \(BD\) and \(BC\) (assuming the diagram shows the non - common sides forming a straight line) are opposite rays forming a straight line. This matches the definition of a linear pair.

Answer:

linear pair