Question

If in the figure a || b and c || d, then name the angles that are congruent to $\angle 2$.

Answer 1

$\angle 2=\angle 4$ (Vertically opposite angles)

$\angle 2=\angle 6$ (Corresponding angles)

$\angle 6=\angle 8$ (Vertically opposite angles)

$\Rightarrow \angle 2=\angle 8$

$\angle 2=\angle 10$ (Corresponding angles)

$\angle 10=\angle 12$ (Vertically opposite angles)

$\Rightarrow \angle 2=\angle 12$

$\angle 10=\angle 14$ (Corresponding angles)

$\Rightarrow \angle 2=\angle 14$

$\angle 14=\angle 16$ (Vertically opposite angles)

$\Rightarrow \angle 2=\angle 16$

So $\angle 2$ is congruent to $\angle 4,\angle 6,\angle 8,\angle 10,\angle 12,\angle 14$ and $\angle 16$