Question

if δabc ≅ δdec, ∠b = x + 15 and ∠e = 6x - 65. x = ?

Explanation:

Step1: Use property of congruent triangles

Since $\triangle ABC\cong\triangle DEC$, corresponding angles are equal. So $\angle B=\angle E$.

Step2: Set up equation

We have the equation $x + 15=6x-65$.

Step3: Solve for x

Subtract $x$ from both sides: $15 = 6x-x-65$, which simplifies to $15=5x - 65$. Then add 65 to both sides: $15 + 65=5x$, so $80 = 5x$. Divide both sides by 5: $x=\frac{80}{5}=16$.

Answer:

$16$