Inscribed Angles and Intercepted Arcs

Inscribed Angles in Circles

​Learning : You should be able to use the relationships of inscribed angles and their intercepted arcs to determine missing arc and angle measures as well as solve algebraic expressions.

Match

Let's review our vocabulary first!

Match the vocabulary words to their definitions.

• an unbroken part of a circle

• formed when two straight lines or rays meet at a common endpoint

• an angle whose vertex is ON the circle

• an arc that is encased on either side by two different segments whose endpoints are also endpoints of an inscribed angle

arc

angle

inscribed angle

intercepted arc

• arc

• angle

• inscribed angle

• intercepted arc

Labelling

Label each of the highlighted parts of the circle with the correct vocabulary word.

Drag labels to their correct position on the image

angle

arc

inscribed angle

intercepted arc

Let's see if you can determine the relationship between inscribed angles and their intercepted arcs.
1. Look at the following examples.
2. Jot down what you notice.

Open Ended

What did you notice about the inscribed angles and their intercepted arcs?

What have we discovered?
The measure of an inscribed angle is 1/2 its intercepted arc.

Open Ended

The inscribed angle being half the measure of the intercepted arc is the same as saying, "The intercepted arc is ___________ the inscribed angle".

What would you fill in the blank with?

​

​

Given the measure of the intercepted arc...

to find the measure of the intercepted arc, we will:
Multiply the inscribed angle by 2

​Given the measure of the inscribed angle...

To find the measure of an inscribed angle or an intercepted arc, we will see what we are given and then make a decision.

to find the measure of the inscribed angle, we will:
Multiply the intercepted arc by 1/2
OR
Divide the intercepted arc by 2

Let's do some examples!

Math Response

Determine the measure of the missing inscribed angle.

Type answer here

Correct Answer: 84

Deg^°

Rad

Math Response

Determine the measure of the missing intercepted arc.

Type answer here

Correct Answer: 98

Deg^°

Rad