Question

chords and arcs

find the value of x.

(x = ?^{\circ})

Explanation:

Identify congruent chords

The circle shows two chords, each having a length of \(8\).

Apply Congruent Chords Theorem

In a circle, if two chords are congruent (equal in length), then their corresponding minor arcs are also congruent (equal in measure).

Solve for x

Since both chords have a length of \(8\), the arc corresponding to the first chord, which measures \(52^\circ\), must be equal in measure to the arc corresponding to the second chord, which measures \(x^\circ\).

$$ x = 52 $$

Answer:

Find the value of x.
\(x =\) <blank>52</blank>\(^\circ\)