Question

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

Explanation:

Step1: Apply equal - arc property

Since $\angle BAE\cong\angle DAE$, the arcs they intercept are equal. So, the chords opposite these arcs are equal. That is, $3x - 24=x + 10$.

Step2: Solve the equation

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