Question

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

m∠1=1/2(mAB−mEF)

m∠1=1/2(mAB+mEF)

m∠1=1/2mAB

m∠1=mAB+mEF

Answer 1

`m\angle 1 = (1)/(2)(m\angle AB+m\angle EF)`

Explanation:

When two chords intersect each other inside a circle, the measure of the angle formed is one half the sum of the measure of the intercepted arcs.

Here, the chords FA and BE intersected each other inside the circle,

Also, angle 1 is the angle formed by the intersection,

Thus, from the above statement,

`m\angle 1 = (1)/(2)(m\angle AB+m\angle EF)`

Second option is correct.

Answer 2

m∠1=1/2(mAB+mEF)

Explanation:

The measure of the angle is half the sum of the intercepted arcs.