Question - Angle Bisector Calculation
Solution:
The image shows a geometric figure with points A, M, O, and B, where O is the vertex of the angle. The point M is located on the bisector of the angle AOB. The following angle measures are indicated on the figure:- $$ \angle AOM $$ = $$ x + 12^\circ $$- $$ \angle MOB $$ = $$ 3x - 8^\circ $$Since M is on the bisector of the angle AOB, the angles AOM and MOB should be equal. Therefore, we have:$$ x + 12^\circ = 3x - 8^\circ $$Now, let's solve for x:$$ x + 12^\circ + 8^\circ = 3x $$$$ x + 20^\circ = 3x $$$$ 20^\circ = 3x - x $$$$ 20^\circ = 2x $$$$ x = 20^\circ / 2 $$$$ x = 10^\circ $$The value of x is $$ 10^\circ $$.
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