Question

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

1. multiply the angle measure by 2.

2(m∠abc) = 56°

1. 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.
m∠abc = 28°
m(widehat{ac}) = 80°
m(widehat{de}) = 24°

Explanation:

Step1: Recall the formula

The formula for the measure of the angle formed by two intersecting secants is $m\angle ABC=\frac{1}{2}(m\overparen{AC}-m\overparen{DE})$, which can be rewritten as $m\overparen{AC}-m\overparen{DE} = 2\times m\angle ABC$. So the difference of arc - measures always equals 2 times the angle measure.

Answer:

2