Question

question 1 of 10
in the diagram below, \\( \overline { d e } \\) and \\( \overline { e f } \\) are tangent to \\( \odot o \\). which equation could be solved to find \\( x \\), the measure of \\( \overparen { d f } \\) ?

\\( \bigcirc \\) a. \\( \frac { 1 } { 2 } ( 228 + x ) = 48 \\)
\\( \bigcirc \\) b. \\( \frac { 1 } { 2 } ( 228 - x ) = 48 \\)
\\( \bigcirc \\) c. \\( \frac { 1 } { 2 } ( 228 - 48 ) = x \\)
\\( \bigcirc \\) d. \\( \frac { 1 } { 2 } ( 228 + 48 ) = x \\)

Explanation:

Step1: Recall the formula for the measure of an angle formed by two tangents

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

Step2: Identify the intercepted arcs

The angle \( \angle DEF = 48^{\circ}\), the intercepted arcs are \(228^{\circ}\) and \(x^{\circ}\).
Using the formula \(m\angle DEF=\frac{1}{2}(m\overset{\frown}{GF}-m\overset{\frown}{DF})\)
Substitute the values: \(48=\frac{1}{2}(228 - x)\)

Answer:

B. \(\frac{1}{2}(228 - x)=48\)