Question

tangent-secant #1 unique id: 1012
this is the only question in this section.
question
solve for x.
answer attempt 2 out of 3
additional solution no solution
x = submit answer

Explanation:

Step1: Apply the tangent - secant angle formula

The measure of an angle formed by a tangent and a secant is half the difference of the measures of the intercepted arcs. The formula is \(\angle R=\frac{1}{2}(\text{major arc}-\text{minor arc})\). Here, the angle formed by the tangent \(RS\) and the secant \(QR\) is \(\angle R = 6x + 4\), and the intercepted arcs: assume the minor arc is \(92^{\circ}\) and the major arc is \(360^{\circ}-92^{\circ}=268^{\circ}\). Then \(6x + 4=\frac{1}{2}(268 - 92)\).

Step2: Simplify the right - hand side of the equation

First, calculate \(\frac{1}{2}(268 - 92)\). \(268-92 = 176\), and \(\frac{1}{2}\times176=88\). So the equation becomes \(6x+4 = 88\).

Step3: Solve for \(x\)

Subtract \(4\) from both sides of the equation: \(6x=88 - 4\). Then \(6x=84\). Divide both sides by \(6\): \(x=\frac{84}{6}\).

Answer:

\(x = 14\)