Question

In the diagram below, DE and EF are tangents to O. Which equation could be solved to find y, the measure of DGF?

Answer 1

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

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

Answer 2

The value of y will be evaluated as follows:
For angle formed outside of circle by intersection:
Two tangents or two secants or a tangent and a secant, the formula for angle formed outside will be:
Angle formed outside=1/2(Difference of Intercepted Arcs)
thus from this situation:
angle formed outside is ∠DEF=53°
intercepted arcs are y and 127°
hence
53=1/2(y-127)
The answer is:
C] 1/2(y-127)=53