Circumscribed Angles

Circumscribed Angles and Beyond

Tangent Chord Angle

Vertex is on the edge of the circle.

Same equation as inscribed angle.

 $arc=2\angle$  

Tangent Chord Angle

Vertex is on the edge of the circle.

Same equation as inscribed angle.

 $arc=2\angle$  

Tangent Chord Angle Example 1

If arc CDB = 218 degrees, what is the measure of angle BCW?

Tangent Chord Angle Example 1

If arc CDB = 218 degrees, what is the measure of angle BCW?

 $arc\ =\ 2\angle$  

 $218=2\angle$  

Tangent Chord Angle Example 1

If arc CDB = 218 degrees, what is the measure of angle BCW?

 $arc\ =\ 2\angle$  

 $\frac{218}{2}=\frac{2\angle}{2}$  

Tangent Chord Angle Example 1

If arc CDB = 218 degrees, what is the measure of angle BCW?

 $arc\ =\ 2\angle$  

 $109=\angle BCW$  

Multiple Choice

If the measure of arc TKG = 277 degrees, what is the measure of angle BGT?

• 139

• 554

• 138.5

• 97

Circumscribed Angle

The vertex of the angle is outside of the circle.

 $2\angle=big-small$  

Circumscribed Angle

The vertex of the angle is outside of the circle.

Solving for an angle:
 $\angle=\frac{big-small}{2}$ 



Solving for an arc: 
 $2\angle=big-small$  

Circumscribed Angle Example 2

The measure of arc GH = 60 degrees. The measure of arc EF is 140 degrees. What is the measure of angle D?

Circumscribed Angle Example 2

The measure of arc GH = 60 degrees. The measure of arc EF is 140 degrees. What is the measure of angle D?

 $\angle=\frac{big-small}{2}$  

$$
\angle=\frac{140-60}{2}

Circumscribed Angle Example 2

The measure of arc GH = 60 degrees. The measure of arc EF is 140 degrees. What is the measure of angle D?

 $\angle=\frac{big-small}{2}$  

$$
\angle=\frac{140-60}{2}

Circumscribed Angle Example 2

The measure of arc GH = 60 degrees. The measure of arc EF is 140 degrees. What is the measure of angle D?

 $\angle=\frac{big-small}{2}$  

 $\angle=40$  

Circumscribed Angle Example 3

The measure of Angle D is 35 degrees. The measure of arc EF is 150 degrees. What is the measure of arc GH?

 $2\angle=big-small$  

 $2\left(35\right)=150-GH$  

Circumscribed Angle Example 3

The measure of Angle D is 35 degrees. The measure of arc EF is 150 degrees. What is the measure of arc GH?

 $2\angle=big-small$  

 $70=150-GH$  
-150      -150

Circumscribed Angle Example 3

The measure of Angle D is 35 degrees. The measure of arc EF is 150 degrees. What is the measure of arc GH?

 $2\angle=big-small$  

 $70=150-GH$  
-150      -150

 $-80=-GH$  

Circumscribed Angle Example 3

The measure of Angle D is 35 degrees. The measure of arc EF is 150 degrees. What is the measure of arc GH?

 $2\angle=big-small$  

 $70=150-GH$  
-150      -150

 $80=GH$  

Multiple Choice

What is the measure of angle S?

• 69

• 35

• 138

• 34.5

Multiple Choice

What is the measure of angle S?

• 51.5

• 128.5

• 79

• 103