Question

select all the correct answers.
two parallel lines are cut by two transversals, which are also parallel to each other, as shown in the figure.
which angles are congruent to angle n?

Explanation:

Step1: Identify vertical angles

Vertical angles are congruent. Angle \(N\) and angle \(Q\) are vertical angles. So \(N\cong Q\).

Step2: Use properties of parallel lines (corresponding angles)

Since the two parallel lines are cut by parallel transversals, corresponding angles are congruent. Angle \(N\) and angle \(F\) are corresponding angles. So \(N\cong F\).
Angle \(N\) and angle \(A\) are also corresponding angles (by the parallel - line and transversal relationships). So \(N\cong A\).

Step3: Use vertical angles again for related angles

Angle \(A\) and angle \(C\) are vertical angles (\(A\cong C\)), so \(N\cong C\) (by transitive property since \(N\cong A\)).
Angle \(F\) and angle \(G\) are vertical angles (\(F\cong G\)), so \(N\cong G\) (by transitive property since \(N\cong F\)).
Angle \(Q\) and angle \(R\) are vertical angles (\(Q\cong R\)), so \(N\cong R\) (by transitive property since \(N\cong Q\)).

Answer:

Angles \(A\), \(C\), \(F\), \(G\), \(Q\), \(R\) are congruent to angle \(N\).