Question

http://prntscr.com/o2zpjv

Answer 1

@Hero @Vocaloid

Answer 2

Hi @Nicole do you know the formula for Inscribed Angle?

Answer 3

If so, what is it?

Answer 4

Hello, im not sure could you tell me it?

Answer 5

The formula for inscribed angle is:

\(\boxed{\text{Inscribed Angle} = \dfrac{1}{2}\text{Intercepted Arc}}\)

Answer 6

So in this case, what angle represents the inscribed angle and what is the intercepted arc in this case?

Answer 7

the inscribed angle is x+2 ?

Answer 8

im not sure what the intercepted angle is

Answer 9

Correct, the inscribed angle is C which measures x + 2 degrees. read the question once more. Remember that the inscribed angle is what intercepts the corresponding arc on a circle.

Answer 10

Suppose in this case for example that E represents the intercepted angle. Then CD is the arc.

Answer 11

intercepted arc* that is

Answer 12

would it be 16x?

Answer 13

im not sure what the intercepted arc is

Answer 14

Yes, AB is the intercepted arc which is 16x degrees. So how should we set this up to solve according to the formula?

Answer 15

x+2=1/2(16x) ?

Answer 16

Exactly

Answer 17

x=2/7

Answer 18

Looks right

Answer 19

Okay

http://prntscr.com/o300b2

Answer 20

@Hero

Answer 21

What is the relationship between the central angle and the minor arc that it intercepts?

Answer 22

360-80 ?

Answer 23

You've applied the formula for finding the major arc. What I asked, however, is about the relationship between the central angle and the minor arc.

Answer 24

Let's do it this way: What is the central angle of the circle?

Answer 25

Umm no im not sure

Answer 26

The central angle of the circle is the angle whose vertex is the center of the circle and whose endpoints are on the circle.

Answer 27

Do you see something like that in the given figure?

Answer 28

Yes I do

Answer 29

@Hero

Answer 30

And what is the name of that angle?

Answer 31

C

Answer 32

What is the full name of the angle?

Answer 33

angle ACB?

Answer 34

Correct and what is the name of the arc that this angle intercepts?

Answer 35

Would you like a hint?

Answer 36

Yes please

Answer 37

The endpoints of the angle are also the endpoints of the intercepted arc. For example:
In this case, the angle XZY is the central angle and XY are the endpoints of the angle which are also the endpoints of arc XY.

Answer 38

Also, just so you know, in general, the measure of the central angle is equal to the measure of its intercepted arc.

Answer 39

That applies in the case of the problem we're working on.