Question

question
solve for x

Explanation:

Step1: Use 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 \(\angle MLK=\frac{1}{2}(\text{major arc}-\text{minor arc})\). Here, \(\angle MLK = 5x + 8\), the major arc \(=18x+10\), and the minor arc \( = 74^{\circ}\). So, \(5x + 8=\frac{1}{2}[(18x + 10)-74]\)

Step2: Simplify the right - hand side

First, simplify \(\frac{1}{2}[(18x + 10)-74]\). \(\frac{1}{2}(18x+10 - 74)=\frac{1}{2}(18x-64)=9x-32\). So the equation becomes \(5x + 8=9x-32\)

Step3: Solve for \(x\)

Subtract \(5x\) from both sides: \(8=9x-5x - 32\). Then \(8 = 4x-32\). Add \(32\) to both sides: \(8 + 32=4x\), \(40 = 4x\). Divide both sides by \(4\): \(x = 10\)

Answer:

\(x = 10\)