Question

Help! Pic below I give medals :)
m arc AC=100deg. m∠ADC=25deg. and C is the point of tangency for DE. Find: m∠ACE m arc BC and m arc AFB

Answer 1

The measure of an angle formed by a tangent and a secant that intersect outside the circle is half the difference of the arcs.
In other words, m<D = (1/2)(m arc AC - m arc BC)
Since you know m<D and m arc AC, you can easily get m arc BC.
Once you have m arc BC, you can find m arc AFB

The measure of an angle formed by a tangent and a chord and whose vertex is a point on the circle is half the measure of the intercepted arc.
That means m<ACE = (1/2)m arc AC

Answer 2

25=m<BC

Answer 3

m<ACE=50

Answer 4

m<ADC = 25 = m<D
m arc AC = 100

m<D = (1/2)(m arc AC - m arc BC)
25 = (1/2)(100 - m arc BC)
50 = 100 - m arc BC
-50 = - m arc BC
m arc BC = 50

Answer 5

so how do I find m∠ACE and m arc AFB

Answer 6

You got m<ACE correct.
m<ACE = (1/2)m arc AC
m<ACE = (1/2)(100)
m<ACE = 50

Answer 7

yes I got that I forgot to simplify

Answer 8

A full circle is an arc of 360 degrees. If m arc AC = 100, and m arc BC = 50, all that's left of the full circle is m arc AFB, so subtract 360 - 100 - 50.