Questions: If triangle ABC is congruent to triangle DEC, angle B = x + 15 and angle E = 6x - 65

Transcript text: If $\triangle A B C \cong \triangle D E C$, $\angle B=x+15$ and $\angle E=6 x-65$

Solution

Solution Steps

Step 1: Identify the Given Information

We are given that triangles $ \triangle ABC $ and $ \triangle DEC $ are congruent. This means that corresponding angles and sides are equal. Specifically, we are given:

$ \angle B = x + 15 $
$ \angle E = 6x - 65 $

Step 2: Set Up the Equation

Since $ \triangle ABC \cong \triangle DEC $, the corresponding angles $ \angle B $ and $ \angle E $ are equal. Therefore, we can set up the equation: \[ x + 15 = 6x - 65 \]

Step 3: Solve for $ x $

To solve for $ x $, we need to isolate $ x $ on one side of the equation: