Question

solve for x.
6x + 3
19x - 6
51°

Explanation:

Step1: Use the formula for the angle formed by a tangent and a secant

The measure of an angle formed by a tangent and a secant outside a circle is half the difference of the measures of the intercepted arcs. The formula is \( \angle K=\frac{1}{2}(\text{major arc}-\text{minor arc}) \). Here, \( \angle K = 51^{\circ} \), the major arc is \(19x - 6\) and the minor arc is \(0^{\circ}\) (since \(KJ\) is a tangent and \(KL\) is a secant, the formula simplifies to \(51=\frac{1}{2}((19x - 6)-0)\)

Step2: Solve the equation for \(x\)

Multiply both sides of the equation \(51=\frac{1}{2}(19x - 6)\) by \(2\):
\(51\times2=19x - 6\)
\(102=19x - 6\)
Add \(6\) to both sides:
\(102 + 6=19x\)
\(108=19x\)
Divide both sides by \(19\):
\(x = 6\)

Answer:

\(x = 6\)