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Studying for a test? Prepare with these 4 lessons on Module 4: Angle measure and plane figures.

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# Decomposing an angle

Video transcript

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.