An Inscribed Angle's

- vertex lies somewhere on the circle
- sides are chords from the vertex to another point in the circle
- creates an arc , called an intercepted arc
- The measure of the inscribed angle is half of measure of the intercepted arc (This only works for the most frequently studied case when the vertex point such as B is not within arc AC.)

Look at the picture above

**Interactive** Inscribed Angle

**Practice**

Identifying the Inscribed Angles and their Intercepted Arcs

If $$ m\angle XYZ =40^{o} $$, what is measure of $$ \overparen{XZ} $$ ?

Measure of inscribed angle = ½ measure of the intercepted arc. Therefore, $$ \overparen{XZ} = 2 \cdot 40^{o}= 80^{o} $$

- YZ
^{2}= 5^{2}+12^{2} - YZ = 13

^{2} +132^{2} ≠ 164^{2}. Since the Pythagorean theorem does not hold, the X is not a right angle and the measure of arc ≠ 180°.