Question

which equation is correct regarding the measure of $angle1$?$\bigcirc mangle1=\frac{1}{2}(a-c)$$\bigcirc mangle1=\frac{1}{2}(a+c)$$\bigcirc mangle1=\frac{1}{2}(b-d)$$\bigcirc mangle1=\frac{1}{2}(b+d)$

Explanation:

Step1: Recall exterior angle theorem

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

Step2: Identify intercepted arcs

The intercepted arcs are the major arc \(b\) and the minor arc \(d\).

Step3: Apply the theorem

The formula for the angle is half the difference of the intercepted arcs:
\(m\angle1 = \frac{1}{2}(b - d)\)

Answer:

\(m\angle1 = \frac{1}{2}(b - d)\) (the third option)