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31 July, 15:24

Unghiurile AOB si BOC sunt adiacente suplementare iar OM si ON sunt bisectoarele lor. Calculati masura unghiului MON, pentru fiecare din situatiile: a)

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  1. 31 July, 16:04
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    The complete question would be:

    The angles AOB and BOC are adjacent. OM and ON are their bisector lines. Calculate their measures to each situations: a) AOB = 60°; b) BOC = 100°.

    a) AOB = 60°

    If angle AOB = 60°, then angles AOM = MOB = 30°, because they are divided by a bisector.

    Also, adjacent angles are on a straight angle, so AOB + BOC = 180°. If AOB = 60°, then BOC = 120°, because that's the difference.

    In addition, BON = NOC = 60°, because they are divided by a bisector line.

    So, basically, MOB + BON = 30° + 60° = 90°, that means MON is a right angle, because its equal to 90° due to the sum MOB + BON = MON.

    b) BOC = 100°

    If angle BOC = 100°, then BON = NOC = 50°, because they are divided by a bisector.

    Also, AOB + BOC = 180°, because they are adjacent on a straight angle.

    So, AOB = 180° - BOC, which is, AOB = 180° - 100° = 80°.

    So, we know that AOM = MOB = 40°, because they are divided by a bisector.

    Lastly, MON = MOB + BON = 40° + 50° = 90°, that is, angle MON is again a right angle.

    Just remember that a bisector line divided an angle in to equal parts.
  2. 31 July, 18:39
    0
    AOB+BOC=180 grade

    =>AOB=80 grade

    MOB=40 grade

    BON=50 grade

    =>MON=90 grade

    Step-by-step explanation:

    answered
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