Question

what part of the proof uses the justification that angles with a combined degree measure of 90° are complementary?

Explanation:

Step1: Analyze the definition of complementary angles

Complementary angles are defined as two angles whose sum is \(90^{\circ}\).

Step2: Check each statement - reason pair

• Statement 1: \(m\angle1 = 40^{\circ}\) (given) - no use of complementary - angle definition.
• Statement 2: \(m\angle2=50^{\circ}\) (given) - no use of complementary - angle definition.
• Statement 3: \(\angle1\) is complementary to \(\angle2\). Since \(m\angle1 + m\angle2=40^{\circ}+50^{\circ} = 90^{\circ}\), and the reason is "definition of complementary angles". This is where the justification that angles with a combined degree measure of \(90^{\circ}\) are complementary is used.
• Statement 4: \(\angle2\) is complementary to \(\angle3\) (given) - no use of the specific justification about the sum of \(90^{\circ}\) for the definition.
• Statement 5: \(\angle1\cong\angle3\) (congruent complements theorem) - no use of the definition of complementary angles based on the sum of \(90^{\circ}\).

Answer:

Statement 3 with the reason "definition of complementary angles"