Question

question 10 of 10
which equation can be solved to find x, the measure of in the diagram below?

a. x + 76 = 185
b. x - 76 = 185
c. \\( \frac { 1 } { 2 } ( 185 + x ) = 76 \\)
d. \\( \frac { 1 } { 2 } ( 185 - x ) = 76 \\)

Explanation:

Step1: Recall the formula for the measure of an angle formed by a tangent and a secant

The measure of an angle formed by a tangent and a secant outside a circle is given by the formula \( \frac{1}{2}(m\overset{\frown}{major}-m\overset{\frown}{minor}) \).

Step2: Identify the major and minor arcs

Here, the major arc is \(185^{\circ}\) and the minor arc is \(x\), and the measure of the angle \( \angle Y = 76^{\circ}\)

Step3: Substitute into the formula

Substituting into the formula \( \angle Y=\frac{1}{2}(m\overset{\frown}{major}-m\overset{\frown}{minor})\), we get \(76=\frac{1}{2}(185 - x)\)

Answer:

D. \( \frac{1}{2}(185 - x)=76 \)