Question

in circle a, $angle bae cong angle dae$.
what is the value of x?
$\bigcirc$ 14
$\bigcirc$ 17
$\bigcirc$ 27
$\bigcirc$ 34
in the circle, chord eb is labeled $3x-24$, chord ed is labeled $x+10$

Explanation:

Step1: Relate congruent angles to chords

In a circle, congruent central angles intercept congruent chords. Since $\angle BAE \cong \angle DAE$, chords $\overline{BE}$ and $\overline{DE}$ are congruent.

Step2: Set chord expressions equal

Set the lengths of the chords equal to each other:
$3x - 24 = x + 10$

Step3: Solve for x

Subtract $x$ from both sides:
$3x - x - 24 = 10$
$2x - 24 = 10$
Add 24 to both sides:
$2x = 10 + 24$
$2x = 34$
Divide by 2:
$x = \frac{34}{2} = 17$

Answer:

17