Question

which of the following statements is correct?
∠abc and ∠fde are supplementary.
∠acb and ∠def are complementary.
∠acb and ∠def are adjacent.
∠abc and ∠def are nonadjacent.

Explanation:

Step1: Recall the definitions

• Adjacent angles: Have a common vertex, a common side, and no common interior points.
• Complementary angles: Sum to \(90^{\circ}\).
• Supplementary angles: Sum to \(180^{\circ}\).
• Non - adjacent angles: Do not have a common vertex and a common side simultaneously.

Step2: Analyze each option

• For \(\angle ABC\) and \(\angle FDE\): There is no information about their sum being \(180^{\circ}\), so they are not necessarily supplementary.
• For \(\angle ACB\) and \(\angle DEF\): There is no information about their sum being \(90^{\circ}\), so they are not necessarily complementary.
• For \(\angle ACB\) and \(\angle DEF\): They do not share a common vertex and a common side, so they are not adjacent.
• For \(\angle ABC\) and \(\angle DEF\): They do not share a common vertex and a common side. By the definition of non - adjacent angles (two angles that do not have a common vertex and a common side), \(\angle ABC\) and \(\angle DEF\) are non - adjacent.

Answer:

\(\angle ABC\) and \(\angle DEF\) are nonadjacent.