Question

in circle a, ∠bae ≅ ∠dae. what is the value of x? o 14 o 17 o 27 o 34 3x - 24 x + 10

Explanation:

Step1: Use congruent - central - angle property

If \(\angle BAE\cong\angle DAE\) in circle \(A\), then the chords opposite these central angles are equal. So, \(BE = DE\).
We have \(BE=3x - 24\) and \(DE=x + 10\).
Set up the equation \(3x-24=x + 10\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(3x-x-24=x - x+10\), which simplifies to \(2x-24 = 10\).
Add 24 to both sides: \(2x-24 + 24=10 + 24\), getting \(2x=34\).
Divide both sides by 2: \(\frac{2x}{2}=\frac{34}{2}\), so \(x = 17\).

Answer:

17