Question

parallel lines m and n are cut by transversal t. which statement is always true? ∠1 and ∠6 are complementary, and ∠3 and ∠7 are congruent. ∠1 and ∠6 are complementary, and ∠3 and ∠7 supplementary. ∠1 and ∠6 are supplementary, and ∠3 and ∠7 are complementary ∠1 and ∠6 are supplementary., and ∠3 and ∠7 are congruent.

Explanation:

Step1: Recall parallel - line properties

When two parallel lines \(m\) and \(n\) are cut by a transversal \(t\), corresponding angles are congruent, and same - side interior angles are supplementary.
\(\angle1\) and \(\angle6\) are same - side interior angles. So, \(\angle1+\angle6 = 180^{\circ}\), which means \(\angle1\) and \(\angle6\) are supplementary.

Step2: Identify corresponding angles

\(\angle3\) and \(\angle7\) are corresponding angles. For parallel lines \(m\) and \(n\) cut by transversal \(t\), corresponding angles are congruent. So, \(\angle3=\angle7\).

Answer:

\(\angle1\) and \(\angle6\) are supplementary, and \(\angle3\) and \(\angle7\) are congruent.