Question

the figure shows lines r, s, and p intersecting to form angles numbered 1, 2, 3, 4, 5, and 6. all three lines lie in the same plane. based on the figure, which of the individual statements would provide enough information to conclude that line r is perpendicular to line p? select all that apply. a. m∠2 = 90° b. m∠6 = 90° c. m∠3 = m∠6 d. m∠1 + m∠6 = 90° e. m∠3 + m∠4 = 90° f. m∠4 + m∠5 = 90°

Explanation:

Step1: Recall perpendicular - line property

Two lines are perpendicular if the angle between them is 90°.

Step2: Analyze option A

If \(m\angle2 = 90^{\circ}\), and \(\angle2\) is the angle formed by lines \(r\) and \(p\), then line \(r\) is perpendicular to line \(p\).

Step3: Analyze option B

If \(m\angle6=90^{\circ}\), and \(\angle6\) is the angle formed by lines \(r\) and \(p\), then line \(r\) is perpendicular to line \(p\).

Step4: Analyze option C

\(m\angle3 = m\angle6\) only tells us that \(\angle3\) and \(\angle6\) are congruent. It does not give any information about whether the angle between \(r\) and \(p\) is 90°.

Step5: Analyze option D

\(m\angle1 + m\angle6=90^{\circ}\) does not directly tell us that the angle between \(r\) and \(p\) is 90°. It just gives a relationship between non - adjacent angles.

Step6: Analyze option E

\(m\angle3 + m\angle4 = 90^{\circ}\) does not directly tell us that the angle between \(r\) and \(p\) is 90°. It gives a relationship between non - adjacent angles.

Step7: Analyze option F

\(m\angle4 + m\angle5=90^{\circ}\) does not directly tell us that the angle between \(r\) and \(p\) is 90°. It gives a relationship between non - adjacent angles.

Answer:

A. \(m\angle2 = 90^{\circ}\), B. \(m\angle6 = 90^{\circ}\)