Question

which equation is correct regarding the measure of ∠1? m∠1 = 1/2 (b - d) m∠1 = 1/2 (b + d) m∠1 = 1/2 (a - c) m∠1 = 1/2 (a + c)

Explanation:

Step1: Recall angle - arc relationship

The measure of an angle formed by two secants of a circle is half the difference of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

The angle $\angle1$ is formed by two secants. The larger intercepted arc is $b$ and the smaller intercepted arc is $d$.

Answer:

$m\angle1=\frac{1}{2}(b - d)$