Angle Bisector Calculation
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 \( 10^\circ \).
