Answer:
- ∠MBL and ∠PBQ
- ∠OBN = 95°
- Neither
Step-by-step explanation:
This is essentially a vocabulary question. You need to know the meanings of ...
- adjacent angles
- linear pair
- vertical angles
- straight angle
and you need to know how angles are named.
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Angles adjacent to MBP will share a side and a vertex. The shared side will be one of ray BM or ray BP. The shared vertex is B.
Adjacent angles to MBP are ...
angle MBL and angle PBQ
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Angle OBN is not a vertical angle with any shown, nor is it part of a linear pair with any angles shown. However, if we assume that LR is a straight line through B, then angle LBR is a "straight angle" and has a measure of 180°.
The angle addition postulate tells us ...
∠NBL +∠OBN +∠OBR = 180°
30° +∠OBN +55° = 180°
∠OBN = 95° . . . . . . . . . . . . subtract 85° from both sides
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No two of BM, BP, BR, BO form a straight line, so the given angles do not form a linear pair or vertical angles. (Neither)
