Question

find the value of x.
(5x + 2)° (7x - 12)°
x = \square

Explanation:

Step1: Set angles equal (congruent chords)

Since chord \(DG\) is perpendicular to \(DE\) and chord \(FG\) is perpendicular to \(FE\), chords \(DE\) and \(FE\) are congruent, so their corresponding inscribed angles are equal:
\(5x + 2 = 7x - 12\)

Step2: Rearrange to solve for \(x\)

Subtract \(5x\) and add 12 to both sides:
\(2 + 12 = 7x - 5x\)
\(14 = 2x\)

Step3: Solve for \(x\)

Divide both sides by 2:
\(x = \frac{14}{2}\)

Answer:

\(7\)