Question

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

Explanation:

Step1: Recall angle - relationship definitions

Supplementary angles add up to 180°. Complementary angles add up to 90°. Vertical angles are congruent and corresponding angles are congruent when two lines are parallel.

Step2: Analyze each option

• Option 1: ∠1 and ∠6 are not supplementary as they are not in a linear - pair or related in a way to sum to 180°.
• Option 2: Since ∠1 and ∠7 are supplementary (a linear - pair), and \(m\angle1 = 34^{\circ}\), then \(m\angle7=180 - 34=146^{\circ}\).
• Option 3: ∠1 and ∠7 are supplementary, not complementary.
• Option 4: ∠1 and ∠3 are vertical angles. Since vertical angles are congruent, if \(m\angle1 = 34^{\circ}\), then \(m\angle3 = 34^{\circ}\).
• Option 5: ∠1 and ∠6 are not corresponding angles.

Answer:

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