In △ABC, the side AB is produced to E and side CA is produced to D. If ∠BAD = 125° and ∠EBC = 100°, then which of the following is true ?

Correct Option: Difference between ∠ABC and ∠ACB is 35°

Step-by-step Explanation:

1. Find $\angle \text{BAC}$:
Since $\text{D-A-C}$ forms a straight line, the angle $\angle \text{BAD}$ and $\angle \text{BAC}$ form a linear pair.
$\angle \text{BAC}+\angle \text{BAD}={180}^{°}$
Given $\angle \text{BAD}={125}^{°}$:
$\angle \text{BAC}={180}^{°}-{125}^{°}={55}^{°}$

2. Find $\angle \text{ABC}$:
Similarly, since $\text{A-B-E}$ forms a straight line, the angle $\angle \text{EBC}$ and $\angle \text{ABC}$ form a linear pair.
$\angle \text{ABC}+\angle \text{EBC}={180}^{°}$
Given $\angle \text{EBC}={100}^{°}$:
$\angle \text{ABC}={180}^{°}-{100}^{°}={80}^{°}$

3. Find $\angle \text{ACB}$:
The sum of interior angles in $△\text{ABC}$ is equal to ${180}^{°}$.
$\angle \text{BAC}+\angle \text{ABC}+\angle \text{ACB}={180}^{°}$
${55}^{°}+{80}^{°}+\angle \text{ACB}={180}^{°}$
${135}^{°}+\angle \text{ACB}={180}^{°}$
$\angle \text{ACB}={180}^{°}-{135}^{°}={45}^{°}$

4. Check the difference between $\angle \text{ABC}$ and $\angle \text{ACB}$:
$\angle \text{ABC}-\angle \text{ACB}={80}^{°}-{45}^{°}={35}^{°}$

Thus, the statement "Difference between ∠ABC and ∠ACB is 35°" is true.