Question

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

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. But the measure of an angle formed by a secant - secant, secant - tangent or tangent - tangent outside a circle is half the difference of the measures of the intercepted arcs. Here, for the angle $\angle1$ formed by two chords intersecting inside the circle, the formula for the measure of the angle formed by two chords intersecting inside a circle is $m\angle1=\frac{1}{2}(c - d)$ (where $c$ and $d$ are the measures of the intercepted arcs).

Answer:

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