Explanation:
If OA is perpendicular to OC then mBy angle addition:
[tex]m\angle AOC=m\angle AOB+m\angle BOC[/tex]
Replacing and solving for x:
[tex]\begin{gathered} 90º=(6x-12)º+(3x+30)º \\ 90º=6x+3x+30-12 \\ 90=9x+18 \\ 9x=90-18=72 \\ x=\frac{72}{9}=8 \end{gathered}[/tex]
With x = 8 we have to replace it into the expression for the measure of angle AOB:
[tex]\begin{gathered} m\angle AOB=6x-12 \\ m\angle AOB=6\cdot8-12 \\ m\angle AOB=48-12 \\ m\angle AOB=36º \end{gathered}[/tex]
Answer:
m
