Decomposing an angle

What is the measure of angle COB? So this is C. This is O. And this is B. So they're telling us, what is the measure of this angle right over here? This is angle COB. And they clearly don't give it to us. We need to figure it out. And what they do give us is they give us the measure of an adjacent angle. This angle is 45-degree angled. Angle DOC is adjacent because it shares this arm, this segment OC with angle COB. And then they give us the combined angle. If you take the two outer arms of the two angles, these two outer segments, if you look at angle BOD, they tell us that that is 70 degrees. So if the measure of the angle made from the two outer arms of these two adjacent angles, the two outer rays, if you kept going out like this, if that's 70 degrees and one of the adjacent angles is 45, then this one right over here must be 70 minus 45. Or another way of thinking about it is this angle, the question mark angle, plus 45 degrees must be equal to 70 degrees. Or that question mark must be equal to 70 degrees minus 45 degrees. So what's this going to be? Well, if it was 70 minus 40, we'd get to 30. But then we have to subtract another 5. So it's going to be 25 degrees. So the measure of angle COB is 25 degrees.