Angle Relationships Instruction/ Assignment/ Quiz

Major arc JL measures 300°. Which describes triangle JLM?

equilateral

What is the length of chord ML?

24 units

What is the perimeter of kite OBDE?

38 units

What is the measure of circumscribed ∠X?

90

Angle X is a circumscribed angle of circle V. Which name best describes figure VWXY?

square

Points E, F, and D are located on circle C. The measure of arc ED is 108°. What is the measure of angle ECD?

108°

The measure of central angle LOP is _______ The length of LP is ______ units The length of MP is _______ units

1. 180 2. 17 3. 15

The measure of arc AB is ___ The measure of angle AOB is_______ The measure of angle BDA is ______

1. 50 2. 50 3. 25

We are given that angle AOB is a central angle of circle O and that angle ACB is a circumscribed angle of circle O. We see that AO ≅ BO because ___________ We also know that AC ≅ BC since _______ Using the reflexive property, we see that ________ Therefore, we conclude that △ACO is congruent to △BCO by the _________

1. all radii of the same circle are congruent 2. tangents to a circle that intersect are congruent 3. side CO is congruent to side CO 4. SSS congruency theorem

Which statements are true? Check all that apply.

1. m = 120° 2. m∠COB = 2(m∠CAB) 3. m∠COB = 120°

Use the diagram to complete the statements. The measure of angle EJB is ________ the measure of angle BOE. The measure of angle BDE is _______ the measure of angle BOE. The measure of angle OED is ______ the measure of angle OBD.

1. one-half 2. 180 minus 3. equal to

Angle BCD is a circumscribed angle of circle A. What is the length of line segment AC?

10 units

Angle BCD is a circumscribed angle of circle A. Angle BCA measures 40°. What is the measure of minor arc BD?

100

The measure of minor arc JL is 60°. What is the measure of angle JKL?

120

What is the measure of angle EFD?

47.5°

Central angle AOB and inscribed angle ACB intercept the same arc. Concave polygon AOBC is formed. The sides of central angles will _______ be congruent. The sides of inscribed angles will _______ be congruent.

- always -sometimes

Which statements are true regarding the relationships between central, inscribed, and circumscribed angles of a circle? Check all that apply.

-A circumscribed angle is created by two intersecting tangent segments. -The measure of a central angle will be twice the measure of an inscribed angle that intercepts the same arc. -The measure of a central angle will be equal to the measure of an inscribed angle when the arc intercepted by the inscribed angle is twice as large as the arc intercepted by the central angle.

Which statements are true? Check all that apply

-The circumscribed angle L has a measure of 49° -If the measure of arc HJ is 98°, the measure of angle HMJ is 98°. -If the measure of arc HJ is 98°, the measure of arc HK is 131°.

Which statements are true regarding the diagram for circle P and the angles created? Check all that apply

-∠DEC is a circumscribed angle -∠BCA is an inscribed angle. -∠APB is a central angle. -PB ≅ PA

Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD. Which statements about the arcs and angles are true? Select three options.

-∠EFD ≅ ∠EGD -ED=FD -m = 120°

The measure of minor arc EF is ______ The measure of angle DAB is _______

1. 109 2. 54.5

The measure of arc LM is _____ The measure of angle MBL is ______ The measure of angle MNL is _______

1. 116 2. 58 3. 64

What is the measure of angle COA?

160

What is the measure of angle OAC if major arc AB measures 220 degrees?

55°

What is the perimeter of kite ACBO?

62 units

Points A, B, C, and D lie on circle M. Line segment BD is a diameter. What is the measure of angle ACD?

67.5°

What is the measure of angle WZY?

71°

Points N, P, and R all lie on circle O. Arc PR measures 120°. How does the measure of angle RNQ relate to the measure of arc PR?

Angle RNQ is equal in measure to arc PR