Angles Inside Outside Circle

3/2: Digital Learning Day- Angles Inside/Outside of a Circle

Complete this digital lesson for a participation grade.

On this practice, you will see 3 types of problems:

• Problems with tangent/chord angles

• Problems with intersecting chord angles

• Problems with the angles of secants and/or tangents that meet outside the circle

Problem Type 1: Tangent/Chord Angles

For these problems, the angle created by the tangent/chord meeting is always 1/2 of the intercepted arc.

Multiple Choice

What is the measure of the (?) angle?

• $$80\degree$$

• $$73\degree$$

• $$45\degree$$

• $$75\degree$$

Multiple Choice

What is the measure of the (?) angle?

• $$58\degree$$

• $$47\degree$$

• $$46\degree$$

• $$59\degree$$

Multiple Choice

What is the measure of the (?) arc?

• $$180\degree$$

• $$236\degree$$

• $$235\degree$$

• $$200\degree$$

Problem Type 2: Intersecting Chord Angles

For these problems, the angle formed by two chords is always 1/2 of the sum (addition) of the intercepted arcs.

Multiple Choice

What is the measure of the (?) arc?

• $$120\degree$$

• $$140\degree$$

• $$95\degree$$

• $$160\degree$$

Multiple Choice

What is the measure of the (?) angle?

• $$75\degree$$

• $$59\degree$$

• $$56\degree$$

• $$86\degree$$

Multiple Choice

What is the measure of the (?) arc?

• $$114\degree$$

• $$110\degree$$

• $$125\degree$$

• $$147\degree$$

Problem Type 3: Angle Formed Outside of Circle by Intersection

For these problems, tangents and/or secants meet outside the circle.

When they meet, the form an angle that is one half the difference of the measures of the intercepted arcs.

Multiple Choice

What is the measure of

$$\angle RST?$$  

• $$60\degree$$  

• $$80\degree$$  

• $$68\degree$$  

• $$75\degree$$  

Multiple Choice

What is the measure of

$$\angle VUT?$$  

• $$85\degree$$  

• $$80\degree$$  

• $$70\degree$$  

• $$55\degree$$  

Multiple Choice

What is the measure of

$$\angle TSR?$$  

• $$65\degree$$  

• $$50\degree$$  

• $$60\degree$$  

• $$70\degree$$  

Multiple Choice

What is the measure of

$$\angle VUT?$$  

• $$43\degree$$  

• $$58\degree$$  

• $$72\degree$$  

• $$73\degree$$  

Multiple Choice

What is the measure of

$$\angle FGH?$$  

• $$57\degree$$  

• $$38\degree$$  

• $$44\degree$$  

• $$43\degree$$  

Multiple Choice

What is the measure of

$$arc\ EC?$$  

• $$60\degree$$  

• $$76\degree$$  

• $$85\degree$$  

• $$42\degree$$