Hey there! :D
We have all the given information.
We know that all the angles added up will equal <AOF.
So, from angle <A to angle <D it is 82 degrees. From <B to <E that is 68. The three top angles are the same measure, the bottom two are the same measure.
Let's let <AOB and <BOC stand for x, and <COD, <DOE, and <EOF stand for y.
We have two equations here.
2x+y= 82
x+2y= 68
We have to switch one thing around.
2x+y=82
Subtract 2x from that.
y=82-2x
Plug that into the other equation.
x+2(82-2x)=68
x+164-4x=68
164-3x=68
-3x= -96
x=32
Now we know that <AOB and <BOC are 32 degrees.
Now plug that in to find y.
2x+y=82
2(32)+y=82
64+y=82
y=18
Now we know the measure of all the smaller angles.
So, here's our last equation: (since we have 3 smaller angles and 2 larger ones)
18y+32x=
18(3)+32(2)= 118
<AOF= 18 degrees
I hope this helps!
~kaikers
