Question

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 secants is given by $\frac{1}{2}(\text{major arc}-\text{minor arc})$. The major arc is the larger arc intercepted by the two secants and the minor arc is the smaller one. Here, the major arc is $110^{\circ}$ and the minor arc is $25^{\circ}$.

Step2: Calculate the measure of angle ABC

Using the formula $\angle ABC=\frac{1}{2}(110 - 25)$. First, subtract the measure of the minor arc from the major arc: $110-25 = 85$. Then, multiply by $\frac{1}{2}$: $\frac{1}{2}\times85=42.5^{\circ}$.

Answer:

$42.5^{\circ}$