Question

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

Explanation:

Step1: Set chords equal (congruent angles)

Since $\angle BAE \cong \angle DAE$, their corresponding chords $\overline{BE}$ and $\overline{DE}$ are congruent. So:
$3x - 24 = x + 10$

Step2: Isolate x terms

Subtract $x$ from both sides:
$3x - x - 24 = 10$
$2x - 24 = 10$

Step3: Solve for x

Add 24 to both sides, then divide by 2:
$2x = 10 + 24$
$2x = 34$
$x = \frac{34}{2} = 17$

Answer:

17