Question

given: \\( \angle 1 \\) is complementary to \\( \angle 2 \\).
\\( \angle 2 \\) is complementary to \\( \angle 3 \\).
prove: \\( m \angle 1 = m \angle 3 \\)
what is the missing statement in step 3 of the proof?
\\( m \angle 1 = m \angle 3 \\)
\\( m \angle 1 + m \angle 2 = 90 ^ { \circ } \\)
\\( m \angle 2 = m \angle 3 \\)
\\( m \angle 2 + m \angle 3 = 180 ^ { \circ } \\)

Explanation:

Step1: Recall the definition of complementary angles

Two angles are complementary if the sum of their measures is \( 90^\circ \). Since \( \angle 1 \) is complementary to \( \angle 2 \), by the definition of complementary angles, we have \( m\angle 1 + m\angle 2 = 90^\circ \).

Step2: Analyze the other options

• Option \( m\angle 1 = m\angle 3 \): This is what we are trying to prove, not the missing statement in step 3.
• Option \( m\angle 2 = m\angle 3 \): There is no information given to support this equality at this step.
• Option \( m\angle 2 + m\angle 3 = 180^\circ \): This would be true for supplementary angles, but we know \( \angle 2 \) and \( \angle 3 \) are complementary, so their sum should be \( 90^\circ \), not \( 180^\circ \).

Answer:

\( m\angle 1 + m\angle 2 = 90^\circ \)