Question

statements

1. ∠boc and ∠cod are complementary angles;

bo intersects ad at point o

1. m∠boc + m∠cod = 90°
2. m∠bod = 90°
3. ∠aob and ∠bod are supplementary angles
4. m∠aob + m∠bod = 180°
5. m∠aob + 90° = 180°
6. m∠aob = 90°
7. m∠aob = m∠bod
8. ∠aob ≅ ∠bod

there is a step missing in the proof. identify where in the proof there is a missing step and what this step should be.
there is a missing step between
reasons

1. given
2. definition of complementary angles
3. substitution property of equality
4. linear pair theorem
5. definition of supplementary angles
6. substitution property of equality
7. subtraction property of equality
8. substitution property of equality
9. definition of congruent angles

because the student did not state m∠boc + m∠cod = m∠

Explanation:

Step1: Analyze the proof steps

We are given a proof - based on angle relationships (complementary and supplementary angles). We need to find the missing step.

Step2: Observe the flow of the proof

From step 3, we know \(m\angle BOD = 90^{\circ}\), and from step 5 we have \(m\angle AOB+m\angle BOD=180^{\circ}\). The step that is likely missing is the combination of the fact that \(\angle BOC+\angle COD=\angle BOD\) (angle - addition postulate).
The missing step should be: \(m\angle BOC + m\angle COD=m\angle BOD\) because of the angle - addition postulate. This step is needed to properly connect the information about the complementary angles (\(\angle BOC\) and \(\angle COD\)) and the angle \(\angle BOD\) used in the rest of the proof.

Answer:

The missing step is between step 2 and step 3, and it should be \(m\angle BOC + m\angle COD=m\angle BOD\) with the reason "angle - addition postulate".