Question

what is the measure of angle abc?
○ 42.5°
○ 67.5°
○ 85°
○ 135°
110°
25°

Explanation:

Step1: Recall secant angle theorem

The measure of an angle formed by two secants outside a circle is half the difference of the measures of the intercepted arcs. The formula is:
$$m\angle ABC = \frac{1}{2}(m\overset{\frown}{AC} - m\overset{\frown}{DE})$$

Step2: Identify intercepted arcs

The intercepted arcs are $\overset{\frown}{AC} = 110^\circ$ and $\overset{\frown}{DE} = 25^\circ$.

Step3: Substitute values into formula

$$m\angle ABC = \frac{1}{2}(110^\circ - 25^\circ)$$

Step4: Calculate the result

$$m\angle ABC = \frac{1}{2}(85^\circ) = 42.5^\circ$$

Answer:

42.5°