Problem 8
Answer: angle LSO and angle MSN
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Explanation:
Vertical angles form when we intersect two line segments, lines, or rays. Vertical angles are opposite one another and they are always congruent.
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Problem 9
Answer: angle LMS and angle SMN
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Explanation:
Adjacent angles share a common line, line segment, or ray. Think of two adjacent rooms sharing a common wall between them. In the case of the answer above, the two angles share the common segment SM (note how S and M are part of LMS and SMN)
When it comes to naming angles, the middle letter is always the vertex of the angle. This is the hinge so to speak. Or you could picture a pair of scissors. For angle LMS, the arms LM and SM are the two blades of the scissors while point M is where the blades meet.
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Problem 10
Answer: angle LSM and angle MSN
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Explanation:
Same idea as problem 9. Now we're making S the middle letter. Something like angle LSM is the same as angle MSL.
In this case, the two adjacent angles form a straight line. We consider these two angles a linear pair.
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Problem 11
Answer: angle LSO and angle OSN
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Explanation:
The term linear pair was discussed back in problem 10. So you could list those two angles again, or you could go with another pair as shown above. All that matters is that they are adjacent angles and they are supplementary angles (they add to 180 degrees). There are many possible answers.
Something like the angle pair angle LOS and angle NOS are adjacent angles, but they aren't supplementary. So we don't meet the condition of a linear pair here.
