Explore the properties of angles and arcs formed by two intersecting secants.

✓ 1. Find the difference of arc measures. #& m\overset{\frown}{\sf AC} - m\overset{\frown}{\sf DE}#& = °

✓ 2. Multiply the angle measure by 2.
2(m∠ABC) = °

✓ 3. Move points A and C to change the angle and arcs and make a conjecture.

The difference of arc measures always equals times the angle measure.

✓ 4. Another way of stating the relationship between arc measures and the angle measure of intersecting secants is

#&m\angle {\sf ABC} = {\large \frac{\sf 1}{\sf 2}}(m\overset{\frown}{\sf AC} - m\overset{\frown}{\sf DE}).#&