Question

critical thinking tell whether the statement is always, sometimes, or never true. complementary angles are adjacent. always sometimes never explain your reasoning. angles that are complementary will always form a right angle. complementary angles sometimes share a common side. complementary angles never share a common vertex. complementary angles cannot share a side.

Explanation:

Step1: Recall definitions

Complementary angles sum to \(90^\circ\). Adjacent angles share a common side and vertex.

Step2: Analyze cases

• Example 1: Two angles in a right triangle (e.g., \(30^\circ\) and \(60^\circ\)) are complementary and adjacent (share a side/vertex).
• Example 2: A \(40^\circ\) angle and a \(50^\circ\) angle not sharing a side/vertex (e.g., one in a triangle, one elsewhere) are complementary but not adjacent.

Thus, complementary angles are sometimes adjacent. For the reasoning: "Complementary angles sometimes share a common side" is correct (since sometimes they do, sometimes not), matching "sometimes" for the statement.

Answer:

For "Complementary angles are adjacent": Sometimes
For the reasoning: The option "Complementary angles sometimes share a common side"