# Central Angles, Inscribed Angles, and their Intercepted Arcs

- Author:
- Rose Neal, Stephanie Stern, shansen, Paulette Sokolowski

- Topic:
- Angles

This lesson is to be used to discover relationships between central angles, inscribed angles and the measure of the intercepted arc.
Follow the directions and answer the questions below.

**Directions:**
o Check on the checkbox to Show Central Angle and its Measure
o Check on the checkbox to Show Arc and its Measure
o Drag points C and D and record at least three measures:

- < 180
^{o} ^{ }= 180^{o}- > 180
^{o}^{}

**Make a conjecture about the relationship between a central angle and its intercepted arc:**

**Directions:**
o Check on the checkbox to Show Inscribed Angle and its Measure
o Drag points E, C and D and record at least three measures:

- < 180
^{o} ^{ }= 180^{o}- > 180
^{o}^{}

**a) Make a conjecture about the relationship between a central angle and an inscribed angle. b) Make a conjecture about the relationship between an inscribed angle and its interecepted arc.**