Question

circle x is shown in the diagram.
which equation can be used to solve for $m\angle1$
$m\angle1=\frac{1}{2}(a - b)$
$m\angle1=\frac{1}{2}(a + b)$
$m\angle1=\frac{1}{2}(c - d)$
$m\angle1=\frac{1}{2}(c + d)$

Explanation:

Step1: Recall intersecting chords angle rule

The measure of an angle formed by two intersecting chords inside a circle is half the sum of the measures of the intercepted arcs.

Step2: Identify intercepted arcs for ∠1

∠1 intercepts arcs \(a\) and \(b\).

Step3: Apply the rule to ∠1

The formula is \(m\angle1 = \frac{1}{2}(a + b)\)

Answer:

\(m\angle1 = \frac{1}{2}(a + b)\) (the second option)