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### Course: High school geometry>Unit 8

Lesson 2: Arc measure

# Finding arc measures with equations

Sal solves a few items where arc measures are given in equations, we have to find a variable, then use it to find an arc measure.

## Want to join the conversation?

• At , Sal says that (4k+159) is vertical to (2k+153). How can we tell if they are vertical if we are not given any diameter? Did we assume it was vertical since they are directly across from each other ("eye-balling it")?
• It's given by the definition of a diameter. A segment that touches both sides of a circle, passing through the center. The center, also by definition, is what names the circle - in this case circle P. Hence, BD and AC are diameters. When two or more lines intersect, they form angle relationships (in this case they are vertical)
• In the second problem, why is it okay to assume that arc BC Is the minor arc? Isn't the minor arc supposed to be explicitly stated as BAC?
• A minor arc is always denoted by two letters while a major arc is represented by three. BC would be the name of the minor arc. If you wanted to describe the major arc, you would have to add a another point on the circle because all major arc have three pointts. All major arcs are greater than 180 degrees, semicircles are 180 degrees, and minor arcs are less than 180 degrees.
• im confused if the minor arc in the first example only goes through 2 points on the circle why is the arc in the second exsmple go from b through a, then to c??
• Even though I'm a couple of years late, I'll do this for other people that may need the help, because I've seen this question pop up a couple of times.

Whenever two points are mentioned, then NO MATTER what, it will always be the minor arc. If there is a point in between the minor arc but isn't mentioned, nothing changes. Sometimes questions may show that to throw you off. Whenever three points are mentioned, then I'm pretty sure it's always the major arc. Whenever a circle is split in half, and you are asked about two points, that would just be a semi/half - circle. Hope this helped!
• At Sal says we assume minor arc, but it looks like the minor arc would be identified BAC. BC would be the path with no other letters, which happens to be the long way around. *Are we always to assume the short path with a two letter arc description?*
• Good question. I'm probably really late, so you might know this already, but BC has an angle measure of less than 180. We can assume this, but there is a long hard proof. Because the angle measure is less than 180, that makes it a minor arc. And for a minor arc, you would list the 2 endpoints, nothing in between. And yes, most of the time, we can assume the short path with a 2 letter arc description.
• this does not prepare you for the practice questions at all
• For the second question, it should be measure of BC. However, he got the answer for the measure of BAC. It should be the opposite angle.??
• The measure of BC is the same as the measure of BAC.(since it's the same angle)
(1 vote)
• Aren't you able to just add all the angles together, Put it equal to 360 and solve for the variable?
• In the first example, no, because we don't have expressions for all of the angles, just two of them.

In the second example, yes, and that's exactly what Sal did.
• At , Sal says that (4k+159) is vertical to (2k+153). How can we tell if they are vertical if we are not given any diameter? Did we assume it was vertical since they are directly across from each other ("eye-balling it")?
• I can't do it can someone please explain? I get close to the answers but not correct.
• When you say get close, is that just a matter of how to round numbers or is off more than just rounding, or is it getting the math wrong and happening to get close? These mostly go back to our Algebra I skills of solving problems.
(1 vote)
• At , Sal says to us "but since they gave us just B and C, we can assume this is going to be the minor arc..." (He also does this again at .)
If there's one thing I've learned from taking geometry in 7th grade, its that it's never safe to assume.*
So [this might sound a little weird]... unless geometry is assumptions, how do we know this is right?

[By the way, I understand how this is correct, but is the answer always an assumption or is there a *TRUE