Since ∠AOB is a right angle, it is 90∘. ∠AOB is supplementary to ∠BOC, so m∠AOB+m∠BOC=180∘. By the substitution property of equality, 90∘ +m∠BOC=180∘. Applying the subtraction property of equality, m∠BOC=90∘.

What statement is missing from the proof?

**A.**

∠COD and ∠AOD form a linear pair.

**B.**

∠DOA and ∠BOC are vertical angles.

**C.**

∠AOB and ∠DOC are vertical angles.

**D.**

∠AOB and ∠BOC form a linear pair.

The missing statement in the proof is:

**D.** ∠AOB and ∠BOC form a linear pair.

### Explanation:
A linear pair of angles are adjacent angles whose non-common sides form a straight line. In this case, the angles ∠AOB and ∠BOC are adjacent and together form a straight line at point O. Since linear pairs are supplementary, the proof needs this to establish that the sum of their measures is 180°, which leads to the given conclusion.

Do you want any further details or clarification?

Here are 5 questions to deepen understanding:
1. What are the properties of linear pairs of angles?
2. How can we prove that two angles are supplementary?
3. What other types of angles share a similar property to linear pairs?
4. How does the substitution property of equality work in geometry proofs?
5. Why are vertical angles always congruent?

**Tip:** When working with angle relationships, identifying key geometric properties like linear pairs and vertical angles is essential for simplifying proofs.

Since ∠AOB is a right angle, it is 90∘. ∠AOB is supplementary to ∠BOC, so m∠AOB + m∠BOC = 180∘. By the substitution property of equality, 90∘ + m∠BOC = 180∘. Applying the subtraction property of equality, m∠BOC = 90∘. What statement is missing from the proof?

A. ∠COD and ∠AOD form a linear pair.
B. ∠DOA and ∠BOC are vertical angles.
C. ∠AOB and ∠DOC are vertical angles.
D. ∠AOB and ∠BOC form a linear pair.

Understand the proof involving supplementary angles and linear pairs. This example covers the angle relationship between ∠AOB and ∠BOC, utilizing key geometric concepts like linear pairs, the substitution property, and the supplementary angle theorem. Suitable for students in Grades 8-10.

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