Question

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

Answer 1

AOB+BOC=180 grade

=>AOB=80 grade

MOB=40 grade

BON=50 grade

=>MON=90 grade

Explanation:

answered

Answer 2

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.