Question

which angle is complementary to \\(\angle 4\\)?

\\(\angle 3\\)
\\(\angle 1\\)
\\(\angle 2\\)
\\(\angle 5\\)

Explanation:

Identify the right angle marker

Using the Vertical Angles knowledge point

$$ \angle 2 \text{ and the angle opposite to it are vertical angles.} $$

The diagram shows a right-angle symbol (square marker) at \(\angle 2\). This means:

$$ m\angle 2 = 90^\circ $$

Determine the opposite right angle

Using the Vertical Angles knowledge point

$$ \angle 2 \text{ and } \angle 4 + \angle 5 \text{ are vertical angles.} $$

Since vertical angles are equal:

$$ m\angle 4 + m\angle 5 = m\angle 2 = 90^\circ $$

Apply the definition of complementary angles

Using the Adjacent Angles knowledge point

$$ \angle 4 \text{ and } \angle 5 \text{ share a common ray and vertex.} $$

Since their measures add up to \(90^\circ\), they are complementary:

$$ m\angle 4 + m\angle 5 = 90^\circ \implies \angle 5 \text{ is complementary to } \angle 4. $$

Answer:

• \(\angle 3\)
• \(\angle 1\)
• \(\angle 2\)
• \(\angle 5\) (Correct answer)