Circle O is shown. 2 secants intersect at a point outside of the circle to form angle 1. The first arc formed is d, and the second arc formed is b. Arcs a and c are the other 2 arcs outside of the secants.
Which equation is correct regarding the measure of ∠1?

m∠1 = One-half(a – c)
m∠1 = One-half(a + c)
m∠1 = One-half(b – d)
m∠1 = One-half(b + d)

C    i think you have to use the formula    hope this helps!   :)

Step-by-step explanation:

Circle O is shown. 2 secants intersect at a point outside of the circle to form angle 1. The first arc formed is d, and the second arc formed is b. Arcs a and c are the other 2 arcs outside of the secants.

Which equation is correct regarding the measure of ∠1?

m∠1 = One-half(a – c)

m∠1 = One-half(a + c)

m∠1 = One-half(b – d)

m∠1 = One-half(b + d)

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4