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## Basic geometry and measurement

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

Lesson 4: Understanding angle measurement

# Angle measurement & circle arcs

Learn to measure angles as part of a circle. Created by Sal Khan.

## Want to join the conversation?

• Is a 0˚ angle the same as a 360˚ angle? •   No, they are not the same. But they are related. They are an example of coterminal angles.
With coterminal angles, they have the same starting side (called the initial side) and ending side (called the terminal side), but they don't get there the same way.

The zero angle (0°) and the full angle (360°) would technically look the same if all you did was draw the initial and terminal sides. But the full angle represents spinning around all the way one time, whereas the zero angle represents not spinning around at all.

Similarly, 360000000° is coterminal with the zero angle and the full angle, but it represents spinning all the way around 1 million times.

So, all angles have coterminal angles by adding some multiple of 360° to them. Same initial side, same terminal side, but how you get there is completely different. •   There are two ways to measure angles.
One is degrees and the other is radians.
There are 180 degrees in a straight line.
There are pi radians in a straight line.
• does an angle have to form when 2 rays share a common endpoint cant it be when 2 line segments share a common endpoint?? • Is 365 a prime number? • Can you have an angle that is more that 360 degrees? • It gets complicated, but here is what I found. This is from a math forum that I found in an internet search.

In mathematics we usually separate angles into "angles of inclination"
and "angles of rotation." If you use the basic ideas of geometry in a
plane, an angle is the "opening" between two rays. This leads to the
names above. But if we talk about angles greater than 360 degrees, this
can not happen "between" two rays. I have never heard anyone give
either of the names to angles greater than 360 because we almost always
are talking about the rotation of an angle in terms of some reference
or stationary ray. Perhaps a more important term would be the term used
in expressing the idea you gave when you wrote "because when you draw
an angle, to indicate that the angle is 425 degrees instead of 65" is
the word COTERMINAL. Mathematically we would say a 425 degree rotation
is coterminal with a 65 degree rotation, and both are coterminal with
a negative 295 degree rotation.

Although I would not say a 425 degree angle is "acute," I would say it
had an acute "reference angle." The purpose of the language is to help
us understand the things which are alike, and those which are
different, so to me, it wouldn't be accurate to just say a 425 degree
angle is acute.

Hope this helps.
• Hey people give me 50+ votes (Please I am begging you) • He says angles are formed when two rays share a common endpoint. But can't they be line segments too? Like, a square doesn't have any rays, but it has angles • How many degrees of 5/6 of circle be
(1 vote) • What does a 360 degree angle look like? • Here is some questions you have that will be answered:

What is the angle measure of an arc circle?

360 degrees
The measure of an arc angle is found by dividing that arc length by the circle's circumference, then multiplying by 360 degrees.

How are arcs measured?

Arc Length | CK-12 Foundation
The measure of an arc is equal to the measure of its corresponding central angle. Below, m D C ^ = 70 ∘ and m G H ^ = 70 ∘ . When you measure an arc in degrees, it tells you the relative size of the arc compared to the whole circle.

What is the relationship between angles and arcs in a
circle?

The measure of an inscribed angle in a circle equals half the measure of its intercepted arc.
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