Question
If ∠MOK and ∠JOM are supplementary angles, then what is the value of x and m∠LOK?
A.
x = 130; m∠LOK = 66°
B.
x = 114; m∠LOK = 50°
C.
x = 66; m∠LOK = 130°
D.
x = 50; m∠LOK = 114°
Answers
GPT-4o mini
To determine the value of \( x \) and \( m\angle LOK \), we need to introduce the relationships given in the problem.
Since \( \angle MOK \) and \( \angle JOM \) are supplementary angles, their sum must equal 180 degrees:
\[
m\angle MOK + m\angle JOM = 180^\circ
\]
If we assume that:
- \( m\angle MOK = x \)
- \( m\angle JOM = 180^\circ - x \)
Additionally, if we have \( m\angle LOK \) associated with either \( \angle MOK \) or \( \angle JOM \), we would need that relationship to calculate \( m\angle LOK \).
Now, looking at the answer choices:
1. **Choice A:** \( x = 130 \) and \( m\angle LOK = 66^\circ \)
2. **Choice B:** \( x = 114 \) and \( m\angle LOK = 50^\circ \)
3. **Choice C:** \( x = 66 \) and \( m\angle LOK = 130^\circ \)
4. **Choice D:** \( x = 50 \) and \( m\angle LOK = 114^\circ \)
We can check each option:
- **For A:** If \( x = 130 \), then \( m\angle JOM = 180 - 130 = 50^\circ\). And if \( m\angle LOK = 66^\circ \), it does not relate directly unless stated.
- **For B:** If \( x = 114 \), then \( m\angle JOM = 180 - 114 = 66^\circ\). If \( m\angle LOK = 50^\circ \), it does not establish direct relevance.
- **For C:** If \( x = 66 \), then \( m\angle JOM = 180 - 66 = 114^\circ\). If \( m\angle LOK = 130^\circ \), it follows \( LOK \) would relate as supplementary to the context.
- **For D:** If \( x = 50 \), then \( m\angle JOM = 180 - 50 = 130^\circ\). If \( m\angle LOK = 114^\circ \), it's not complementary as expected in conventional terms.
Considering the relationships, the best possibilities where \( m\angle LOK + m\angle JOM \) shows supplementary meanings corresponds best to choice **C** with a plausible layout on angles.
Thus, the value of \( x \) aligns to be \( 66 \) with \( m\angle LOK \) pegged at \( 130^\circ \).
**Final answer:** **C. \( x = 66 \); \( m\angle LOK = 130^\circ \)**.
Since \( \angle MOK \) and \( \angle JOM \) are supplementary angles, their sum must equal 180 degrees:
\[
m\angle MOK + m\angle JOM = 180^\circ
\]
If we assume that:
- \( m\angle MOK = x \)
- \( m\angle JOM = 180^\circ - x \)
Additionally, if we have \( m\angle LOK \) associated with either \( \angle MOK \) or \( \angle JOM \), we would need that relationship to calculate \( m\angle LOK \).
Now, looking at the answer choices:
1. **Choice A:** \( x = 130 \) and \( m\angle LOK = 66^\circ \)
2. **Choice B:** \( x = 114 \) and \( m\angle LOK = 50^\circ \)
3. **Choice C:** \( x = 66 \) and \( m\angle LOK = 130^\circ \)
4. **Choice D:** \( x = 50 \) and \( m\angle LOK = 114^\circ \)
We can check each option:
- **For A:** If \( x = 130 \), then \( m\angle JOM = 180 - 130 = 50^\circ\). And if \( m\angle LOK = 66^\circ \), it does not relate directly unless stated.
- **For B:** If \( x = 114 \), then \( m\angle JOM = 180 - 114 = 66^\circ\). If \( m\angle LOK = 50^\circ \), it does not establish direct relevance.
- **For C:** If \( x = 66 \), then \( m\angle JOM = 180 - 66 = 114^\circ\). If \( m\angle LOK = 130^\circ \), it follows \( LOK \) would relate as supplementary to the context.
- **For D:** If \( x = 50 \), then \( m\angle JOM = 180 - 50 = 130^\circ\). If \( m\angle LOK = 114^\circ \), it's not complementary as expected in conventional terms.
Considering the relationships, the best possibilities where \( m\angle LOK + m\angle JOM \) shows supplementary meanings corresponds best to choice **C** with a plausible layout on angles.
Thus, the value of \( x \) aligns to be \( 66 \) with \( m\angle LOK \) pegged at \( 130^\circ \).
**Final answer:** **C. \( x = 66 \); \( m\angle LOK = 130^\circ \)**.