select the correct answer.
given: $ \angle aob $ is a right angle
prove: $ m \angle boc = 90 ^ { \circ } $
since $ \angle aob $ is a right angle, it is $ 90 ^ { \circ } $. $ \angle aob $ is supplementary to $ \angle boc $, so $ m \angle aob + m \angle boc = 180 ^ { \circ } $. by the substitution property of equality, $ 90 ^ { \circ } + m \angle boc = 180 ^ { \circ } $. applying the subtraction property of equality, $ m \angle boc = 90 ^ { \circ } $.
what statement is missing from the proof?
$ \bigcirc $ a. $ \angle doa $ and $ \angle boc $ are vertical angles.
$ \bigcirc $ b. $ \angle cod $ and $ \angle aod $ form a linear pair.
$ \bigcirc $ c. $ \angle aob $ and $ \angle boc $ form a linear pair.
$ \bigcirc $ d. $ \angle aob $ and $ \angle doc $ are vertical angles.

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Accepted Answer

# Explanation:
## Step1: Recall the definition of a linear pair
A linear pair of angles is formed when two adjacent angles are supplementary (their measures add up to $180^{\circ}$).
## Step2: Analyze each option
- Option A: Vertical angles are equal but not necessarily supplementary. $\angle DOA$ and $\angle BOC$ being vertical angles is not relevant to the proof that $m\angle BOC = 90^{\circ}$ based on the given information about $\angle AOB$.
- Option B: $\angle COD$ and $\angle AOD$ forming a linear pair has no connection to the relationship between $\angle AOB$ and $\angle BOC$ which is the focus of the proof.
- Option C: If $\angle AOB$ and $\angle BOC$ form a linear pair, then by the definition of a linear pair $m\angle AOB+m\angle BOC = 180^{\circ}$. Since $m\angle AOB = 90^{\circ}$ (given that $\angle AOB$ is a right - angle), we can substitute into the equation $90^{\circ}+m\angle BOC=180^{\circ}$ and solve for $m\angle BOC$.
- Option D: $\angle AOB$ and $\angle DOC$ being vertical angles is not relevant to the proof involving the relationship between $\angle AOB$ and $\angle BOC$.

# Answer:
C. $\angle AOB$ and $\angle BOC$ form a linear pair.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the definition of a linear pair

Step2: Analyze each option

Answer: