Let's analyze the given angle addition postulate:
[tex]\[ m \angle QRS + m \angle RST = m \angle QRT \][/tex]
We need to derive an angle subtraction postulate from this given relationship.
1. Starting with the angle addition postulate:
[tex]\[ m \angle QRS + m \angle RST = m \angle QRT \][/tex]
2. Express [tex]\(m \angle QRS\)[/tex] in terms of the other two angles:
By rearranging the equation, we get:
[tex]\[ m \angle QRS = m \angle QRT - m \angle RST \][/tex]
3. Express [tex]\(m \angle RST\)[/tex] in terms of the other two angles:
Again, rearrange the original equation to isolate [tex]\(m \angle RST\)[/tex]:
[tex]\[ m \angle RST = m \angle QRT - m \angle QRS \][/tex]
4. Identify the matching option:
By examining the given options:
- Option A: [tex]\( m \angle QRS = m \angle RST \)[/tex]
This is incorrect because it implies the two angles are equal, which isn't necessarily the case.
- Option B: [tex]\( m \angle QRT = m \angle RST - m \angle QRS \)[/tex]
This is incorrect because it incorrectly rearranges the original equation.
- Option C: [tex]\( m \angle RST = m \angle QRT - m \angle QRS \)[/tex]
This is correct because it matches our derived equation.
- Option D: [tex]\( m \angle QRS = m \angle RST - m \angle QRT \)[/tex]
This is incorrect because it rearranges the relationship improperly.
The correct angle subtraction postulate is:
[tex]\[ m \angle RST = m \angle QRT - m \angle QRS \][/tex]
Therefore, the correct answer is:
Option C: [tex]\( m \angle RST = m \angle QRT - m \angle QRS \)[/tex]
