Note that I've just gone ahead and put 40° in for x and 30° in for y. If we just work in the order they tell us things, we're going to scribble all over our diagram before we can fill in any actual NUMBERS for our angle measures. Instead, let's start with the

*last*thing they tell us, since that'll allow us to start putting numbers in right away. If

*OB*bisects angle

*AOD*, then:

Next, we can use the first thing they told us:

*OD*bisects angle

*AOF*. That means angle

*DOF*is going to be 80 as well:

And now we're almost there. Since

*y*was 30°, we know angle

*DOE*is 50°, so fill that in. At this point, we kinda have everything we need. The question asked us for angle BOE, which has to be the sum of

*DOE*(which we just figured out is 50°) and

*BOD*(which we already know is 40°):

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