Question

qe 9. in the figure shown, r || s. if the m∠1 is 34°, which statements are true? select two correct answers. the m∠6 is 34° because corresponding angles are congruent. the m∠3 is 34° because vertical angles are congruent. the m∠7 is 56° because m∠1 and m∠7 are complementary angles. the m∠7 is 146° because m∠1 and m∠7 are supplementary angles. the sum of m∠1 and m∠6 is 180° because they are supplementary angles. clear all

Explanation:

Step1: Recall angle - relationships

When two parallel lines are cut by a transversal, corresponding angles are congruent, vertical angles are congruent, and same - side interior angles are supplementary.

Step2: Analyze each statement

• If \(r\parallel s\) and \(m\angle1 = 34^{\circ}\), \(\angle1\) and \(\angle3\) are vertical angles. So \(m\angle3=m\angle1 = 34^{\circ}\) (vertical angles are congruent).
• \(\angle1\) and \(\angle7\) are same - side interior angles. Since \(r\parallel s\), \(m\angle1 + m\angle7=180^{\circ}\). Given \(m\angle1 = 34^{\circ}\), then \(m\angle7=180 - 34=146^{\circ}\) (same - side interior angles are supplementary).

Answer:

• The \(m\angle3\) is \(34^{\circ}\) because vertical angles are congruent.
• The \(m\angle7\) is \(146^{\circ}\) because \(m\angle1\) and \(m\angle7\) are supplementary angles.