Question

question 7 of 10
in the diagram below, $overline{de}$ and $overline{ef}$ are tangent to $odot o$. which equation could be solved to find $y$, the measure of $widehat{dgf}$?
a. $\frac{1}{2}(y - 53)=127$
b. $\frac{1}{2}(y + 53)=127$
c. $\frac{1}{2}(y - 127)=53$
d. $\frac{1}{2}(y + 127)=53$

Explanation:

Step1: Recall tangent - arc formula

The measure of the angle formed by two tangents to a circle is half the difference of the measures of the intercepted arcs.

Step2: Identify arcs and angle

The angle formed by the two tangents $\angle DEF = 53^{\circ}$, the major arc is $\overset{\frown}{DGF}=y^{\circ}$ and the minor arc is $\overset{\frown}{DF}=127^{\circ}$.

Step3: Apply the formula

Using the formula $\text{Angle}=\frac{1}{2}(\text{Major arc}-\text{Minor arc})$, we get $53=\frac{1}{2}(y - 127)$.

Answer:

C. $\frac{1}{2}(y - 127)=53$