arc IJK and arc ILK

In this section, you will investigate the relationship between two angles that intercept opposite arcs of a circle. Opposite arcs are two arcs that share common endpoints on the circle, but contain different portions of the circle without overlap. In the diagram to the left,and  are opposite arcs, since they both have endpoints of I and J and do not overlap.

Create a table similar to the one below in your notes.

m∠D
m∠F
   
   
   
   

This activity might not be viewable on your mobile device. Interactive exercise. Assistance may be required. Using the applet, https://www.geogebratube.org/student/m7319, move ∠D and ∠F individually. Write at least four of their measures in the table.


Journal Entry: Compare the two angle measures. Describe their relationship. If the radius of the circle changed, would the measures of the angles be affected? Explain.

Interactive popup. Assistance may be required.

Check Your Answer

The measures of the angles are supplementary, they equal 180° because a circle is 360°, the two arcs together form a circle and the inscribed angles are half the measure of the arcs so their total would be 180° which would make them supplementary angles. The length of the radius would NOT affect the measure of the angles since their measurement is based on half the measure of the arc which will always be between 0 and 360 degrees, not the length of the radius.Close Pop Up