lesson thirty-one: what’s your angle?

LESSON THIRTY-ONE:

WHAT’S YOUR ANGLE?

WHAT’S YOUR ANGLE?

• Now that we have talked about inscribed figures, we can delve a bit more into ____________within circles.

WHAT’S YOUR ANGLE?

• In a circle, there are infinitely many combinations of _______________________.

• This is an angle whose ________________ is the _________________ of a circle.

WHAT’S YOUR ANGLE?

• The two arcs that are created when a circle is divided by a central angle are called the ___________________________ and ____________________________.

WHAT’S YOUR ANGLE?

• The _________________is the one on the ______________ of the _________________________________.

• This one has been labeled for you.

XC

AB

WHAT’S YOUR ANGLE?

• The ___________________is the one on the ___________________of the _____________ ____________________________.

• Draw the arc on this circle below!

XC

AB

WHAT’S YOUR ANGLE?

• When naming the ____________________we need only two letters.

• The minor arc below could be named _______ or _______.

XC

AB

WHAT’S YOUR ANGLE?

• The ________________ however, need _______________ letters to be accurately labeled.

• ____________ or ______________ could be names for the ____________ below.

XC

AB

WHAT’S YOUR ANGLE?

• The ___________ of the ____________and ____________arc will always be ________ _____the __________________ which creates them.

WHAT’S YOUR ANGLE?

• When given one, you can find the other by simply, _______________________________ _________________________.

• Furthermore, you can find the ___________ of two non-overlapping arcs by simply ______________ their measures.

WHAT’S YOUR ANGLE?• Sometimes, a circle be divided directly _____

______________.• The result is two _______________________.• All of these have a measure of ____________.• You may apply the same principles we just

discussed to _________________________.

WHAT’S YOUR ANGLE?

• For example, let’s see if we can find ________ _____________below.

X C

A

210

WHAT’S YOUR ANGLE?

• What about arc ____________?

XC

A

B42

WHAT’S YOUR ANGLE?

• Aside from central angles, there are also ________________________.

• This is an angle whose __________ is _______ the circle.

WHAT’S YOUR ANGLE?

• How do you suppose ___________________ and _______________________ are related?

WHAT’S YOUR ANGLE?• The measure of the ___________________

will be __________ of the included ________ ________________.

• Furthermore, if two inscribed angle intercept the same ___________, then they are _____________________.

• Also, an inscribed angle that intercepts a ______________ is a _______________.

WHAT’S YOUR ANGLE?• We will be able to use this information to

solve all kinds of problems.• See if you can find arcs _______ and _______.

40

CB

A

WHAT’S YOUR ANGLE?

• See if you can find arcs ______________ and _____________ below.

• HINT: You may have to draw on some old knowledge.

60

45

B

C

A

WHAT’S YOUR ANGLE?

• Try this…find the central angle!

70

B

C

A

WHAT’S YOUR ANGLE?

• It will help you as you do these problems to fill in _________________________ as you go!

• You might crack the code without even really knowing it!