Question

Oa is perpendicular to oc aob equals 6x minus 12 box equals 3x plus 30 find aob

Answer 1

Step-by-step explanation:

If OA is perpendicular to OC then mBy angle addition:

`m\angle AOC=m\angle AOB+m\angle BOC`

Replacing and solving for x:

`\begin{gathered} 90º=(6x-12)º+(3x+30)º \\ 90º=6x+3x+30-12 \\ 90=9x+18 \\ 9x=90-18=72 \\ x=(72)/(9)=8 \end{gathered}`

With x = 8 we have to replace it into the expression for the measure of angle AOB:

`\begin{gathered} m\angle AOB=6x-12 \\ m\angle AOB=6\cdot8-12 \\ m\angle AOB=48-12 \\ m\angle AOB=36º \end{gathered}`

Answer:

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