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### Course: Basic geometry and measurement > Unit 3

Lesson 6: Decomposing angles# Decomposing an angle

Sal finds the measure of angles by adding or subtracting. Created by Sal Khan.

## Want to join the conversation?

- how can we measure angles of hands of a clock without using a protractor its not given in the syllabus, help me.(18 votes)
- You actually can do it without a protractor. There are 12 numbers on a clock. So the distance between each number is 30 degrees. You can use that to measure the angles.(22 votes)

- how can you tell if its a obtuse angle or a right angle(11 votes)
- An obtuse angle is an angle greater than 90 degrees but less that 180. A right angle, on the other hand, is an angle EXACTLY 90 DEGREES OF MEASURE. Usually, a right angle is marked by a square inside of the angle. Also usually, a geometric problem says "Not drawn to scale" so you can't assume it's 90 degrees.

(Sorry, I'm 5 yrs late)(13 votes)

- Does decomposing mean breaking angles equally? please give me full description. Thanks for answering!(9 votes)
- Hi! Decomposing an angle is when you subtract the interior angle's number of degrees (not really sure how to word it...) from the outer angle's number of degrees. I'll explain the problem Sal does in this video.

It's asking 'what is the measure of angle COB?' This means you have to find out how many degrees angle COB is.

It shows you that the angle between D and B is 70°. It also shows that the angle between D and C is 45.

You would want to subtract the full 70° between D and B minus the interior 45° between D and C to get the angle of COB.

Therefore, COB equals:

70° - 45° = COB -----> Angle COB equals 25°.

Hope this helped! :)(16 votes)

- What does 'adjacent' mean?(9 votes)
- Something that is
**near by**, in this case the angle which is near to the other. so the**45**degree angle is adjacent to the**25**degree angle and their sum is going to be**70**degree.(12 votes)

- is there another way to get the angle(10 votes)
- You can use the trigonometric ratios, but the best way is to use a protractor to measure it. If you really want to know all the ways to calculate an angle, you can go to the trigonometry subject. Good luck(8 votes)

- Can you decompose more than one angle?(9 votes)
- Yes we can classify more than one angle(9 votes)

- Hello. I'm sorry, but is the angles from video are adjacent? Indeed, angles shares vertex and one ray, but other rays need to compose a straight line. Maybe these angles are included? Correct me please if I'm wrong.(7 votes)
- A pair of adjacent angles are angles that, as you said, share a common vertex and one ray, but the incorrect part is that they don't need to create a 180 degree angle (straight line) and they can be considered adjacent as long as they are "next to each other." Good luck!(8 votes)

- at first i think it was hard but its is easy lol(9 votes)
- If it get harder i…

i actually don’t know(2 votes)

- So basically, decomposing an angle is making it into smaller angles that equal the original angle, like a straight angle can be decomposed into supplementary angles?(7 votes)
- Can you use geometry in like sciance(2 votes)
- Yeah of course in science, but im not sure if its in sciance(8 votes)

## 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.