C) 1/2(y-127) = 53

Step-by-step explanation:

When an angle is formed by two secants, a secant and a tangent, or two tangents, the measure of the angle is equal to one-half of the difference between the intercepted arcs.

In this circle, our intercepted arcs are y° and 127°. Their difference would be (y-127). One-half of this would be 1/2(y-127). The angle measure is 53; this gives us

1/2(y-127) = 53

hope this helps c:

we know that

The inscribed angle measures half that of the arc comprising

in this problem

m∠DGF -----> is a inscribed angle

m∠DGF=

we have

substitute

m∠DGF=

we know that

Find the measure of arc DGF

therefore

the answer is

a) the measure of inscribed angle m∠DGF is

b) the measure of arc DGF is

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