Question

which equation correctly describes the relationship between the measures of the angles and arcs formed by the intersecting secants?

$m\angle 1=\frac{1}{2}m\overarc{ab}$

$m\angle 1=\frac{1}{2}(m\overarc{ab}-m\overarc{cd})$

$m\angle 1=m\overarc{ab}+m\overarc{cd}$

$m\angle 1=\frac{1}{2}(m\overarc{ab}+m\overarc{cd})$

Explanation:

Step1: Recall the theorem

When two secants intersect inside a circle, the measure of the angle formed is half the sum of the measures of the intercepted arcs.

Step2: Apply the theorem

For \(\angle1\) formed by two intersecting secants, the formula is \(m\angle1=\frac{1}{2}(m\overarc{AB}+m\overarc{CD})\)

Answer:

\(m\angle1=\frac{1}{2}(m\overarc{AB}+m\overarc{CD})\) (the fourth option)