Practice: Circumscribed Angles and Inscribed Quadrilaterals

Practice: Circumscribed Angles and Inscribed Quadrilaterals

2/26/21- Participation Grade

Reminder:

Circumscribed angles have a vertex that is outside the circle. These angles are made of two tangent lines.

What happens when you connect an inscribed angle to two radii?

The central angle and the circumscribed angle are SUPPLEMENTARY. Here, you can see that the central angle is 150° and the circumscribed angle is 30°.

150°+30°=180°

Time to practice!

Can you answer these questions about circumscribed angles?

Multiple Select

Which images show circumscribed angles? Select all that apply.

Multiple Choice

Circumscribed angles are made up of two

• Secant lines

• Tangent lines

• Radii

• Chords

Multiple Choice

What is true about

 $\angle CAB$   and  $\angle CDB$  ? 

• They are supplementary.

• They are complimentary.

• They add up to  $360\degree$ .

• They are congruent.

Multiple Choice

What is the measure of  $\angle CDB$  ?

•  $60\degree$  

•  $300\degree$  

•  $120\degree$  

•  $30\degree$  

Multiple Choice

What is the measure of  $\angle CAB$  ?

•  $226\degree$  

•  $134\degree$  

•  $44\degree$  

•  $46\degree$  

Multiple Choice

If  $\angle CDB=115\degree$  , what is the measure of  $\angle CAB?$  

•  $115\degree$  

•  $65\degree$  

•  $245\degree$  

•  $25\degree$  

Multiple Choice

How would you set up an equation to solve for x?

• $4x+238=2x+146$

• $4x+238+2x+146=360$

• $4x+238+2x+146=180$

• $4x+238+2x+146=90$

Reminder:

What are inscribed quadrilaterals?

These are 4-sided figures inside a circle, with vertices that perfectly touch the edges of the circle.

What do we know about the angles of inscribed quadrilaterals?

We know that the opposite angles are always supplementary. Here, you can see that ∠C and ∠E are opposite angles. ∠C=79° and ∠E=101°.

79°+101°=180°

Multiple Select

Which images show inscribed quadrilaterals? Select all that apply.

Multiple Choice

Which of the following is true about the angles of inscribed quadrilaterals?

• Consecutive angles are supplementary.

• Opposite angles are supplementary.

• Opposite angles are congruent.

• Opposite angles are complimentary.

Multiple Choice

What is the measure of $\angle z?$  

•  $93\degree$  

•  $58\degree$  

•  $106\degree$  

•  $87\degree$  

Multiple Choice

What is the measure of $\angle y?$  

•  $109\degree$  

•  $71\degree$  

•  $80\degree$  

•  $151\degree$  

Multiple Choice

How would you set up an equation to solve for x?

• 4x+9=3x+3

• 4x+9+3x+3=360

• 4x+9+3x+3=180

• 4x+9+3x+3=90

Multiple Choice

Solve for x.

• x=24

• x=7

• x=168

• x=24.4

Multiple Choice

Solve for x.

• x=25

• x=6

• x=107

• x=35