Question

which of the following angles is not congruent to ∠6? ∠2 ∠3 ∠1 ∠7

Explanation:

Step1: Vertical angles

Vertical angles are congruent. $\angle 6$ and $\angle 8$ are vertical angles, so $\angle 6\cong\angle 8$.

Step2: Corresponding angles

Corresponding angles are congruent. $\angle 6$ and $\angle 2$ are corresponding angles, so $\angle 6\cong\angle 2$.

Step3: Alternate exterior angles

Alternate exterior angles are congruent. $\angle 6$ and $\angle 7$ are alternate exterior angles, so $\angle 6\cong\angle 7$.

Step4: Check $\angle 3$

$\angle 3$ and $\angle 6$ are neither vertical, corresponding, nor alternate exterior angles. $\angle 3$ and $\angle 6$ are not congruent.

Answer:

$\angle 3$