1. Arcs and Angles Continued
Lesson 9.2B
R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles

2. Review
The measure of a central angle is equal to the measure of its intercepted arc
The measure of an inscribed angle is one half the measure of its intercepted arc
A tangent line is always perpendicular to a radius drawn to the point of tangency.

3. What if the angles are neither central nor inscribed?
Are the arc measures the same? Are the angle measures the same? What do we do???
30°
80° x°

4. Angles of Intersecting Secants (Internal)
If two secants intersect in the interior of the circle, the measure of an angle formed is half the sum of the measures of the intercepted arcs of the angle and its vertical angle.
In other words… b a x°

5. Now You Try… Example Find the value of x. Find the value of x. 44° x°
66°
44° x°
52°
38° x°

6. Angles of Intersecting Secants (External)
If two secants or tangents intersect in the exterior of a circle, the measure of an angle formed is half the difference of the measures of the intercepted arcs.
In other words… a° b° x°

7. Example Now You Try… Find the value of x. Find the value of x. x° 80°
180°
60° x°
80°
180°
80° x°
70°

8. Example Now You Try… Find the value of x. Find the value of x. x° 120°
105°
95° x°
120°
50o x°

9. Example Now You Try… Find the value of x. Find the value of x. 215° x°
80° x°
215° x°