In the given figure, $AOB$  is a straight line. If  $\angle AOC=4x°$  and  $\angle BOC=5x°$ , then from the following choices, find the value of $\angle AOC$ .

It is given that $AOB$  is a straight line.
We have to find the value of $\angle AOC$ . 
From the diagram,
$\angle AOC=4x°$  and 
$\angle BOC=5x°$ .
The sum of angles on a straight line is equal to ${180}^{°}$ , hence, 
$\angle AOC+\angle BOC={180}^{°}$ .
Substituting and calculating the above equation to get the value of $x$ ,
$\angle AOC+\angle BOC={180}^{°}$ 
$4x+5x={180}^{°}$ 
$9x={180}^{°}$ 
$x=20°$ 
Calculate the value of $4x$  to get $\angle AOC$ . 
$\angle AOC=4x$ 
$\begin{array}{l}=4(20°) \\ =80° \end{array}$ 
The value of $\angle AOC$  is $80°$ .
Hence option 3) is correct.