Question

circle x is shown in the diagram. which equation can be used to solve for m∠1? o m∠1 = 1/2(a - b) o m∠1 = 1/2(a + b) o m∠1 = 1/2(c - d) o m∠1 = 1/2(c + d)

Explanation:

Step1: Recall angle - arc relationship

The measure of an angle formed by two chords intersecting inside a circle is half the sum of the measures of the intercepted arcs. Angle $\angle1$ is formed by two chords intersecting inside circle $X$. The intercepted arcs are $a$ and $b$.

Step2: Apply the formula

The formula for the measure of an angle formed by two chords intersecting inside a circle is $m\angle1=\frac{1}{2}(a + b)$.

Answer:

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