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