Question

central angles
in circle a, ∠bae ≅ ∠dae.
what is the value of x?
14
34
27
17

Explanation:

Step1: Identify Congruent Chords

Since \( \angle BAE \cong \angle DAE \), chords \( BE \) and \( DE \) are congruent (congruent central angles imply congruent chords). Thus, \( 3x - 24 = x + 10 \).

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( 2x - 24 = 10 \).
Add 24 to both sides: \( 2x = 34 \).
Divide by 2: \( x = 17 \).

Answer:

17