Question

finding angle measures involving two intersecting secants what is the measure of angle abc? 42.5° 67.5° 85° 135° 110° 25°

Explanation:

Step1: Recall the secant - secant angle formula

The measure of an angle formed by two intersecting secants outside a circle is given by $\frac{1}{2}(m\overset{\frown}{AC}-m\overset{\frown}{DE})$.

Step2: Identify the arc measures

We are given that $m\overset{\frown}{AC} = 110^{\circ}$ and $m\overset{\frown}{DE}=25^{\circ}$.

Step3: Calculate the angle measure

Substitute the arc - measures into the formula: $\angle ABC=\frac{1}{2}(m\overset{\frown}{AC}-m\overset{\frown}{DE})=\frac{1}{2}(110 - 25)$. First, calculate the value inside the parentheses: $110-25 = 85$. Then, $\frac{1}{2}\times85=42.5^{\circ}$.

Answer:

$42.5^{\circ}$