Question

6 numeric 1 point if arc ( j k=(7 x - 39)^{circ} ) and arc ( m l = 87^{circ} ), find ( x ). answer

Explanation:

Step1: Use the property of congruent chords

In a circle, if two chords are congruent, then their corresponding arcs are congruent. Since chords \(JK\) and \(ML\) are congruent (marked with the same tick - mark), arc \(JK\) is congruent to arc \(ML\). So, we can set up the equation \(7x - 39=87\).

Step2: Solve the equation for \(x\)

Add \(39\) to both sides of the equation:
\(7x-39 + 39=87 + 39\)
\(7x=126\)
Divide both sides by \(7\):
\(x=\frac{126}{7}\)

Answer:

\(18\)