Question

select all the correct answer.
given the degree measures, which statements are true?
image of angle diagram with op, qr, and a transversal t, showing 90° angles
□ op will intersect to qr.
□ t is parallel to op.
□ t is perpendicular op and qr.
□ op is parallel to qr.

Explanation:

Step1: Analyze ∠1 and ∠8 (90°)

∠1 = 90° (given), ∠8 = 90° (given). So line \( t \) (the vertical line) forms right angles with \( \overline{OP} \) and \( \overline{QR} \).

Step2: Check \( \overline{OP} \) and \( \overline{QR} \)

Since \( t \perp \overline{OP} \) and \( t \perp \overline{QR} \), by the theorem that if two lines are perpendicular to the same line, they are parallel, \( \overline{OP} \parallel \overline{QR} \). Also, \( t \) is perpendicular to both (as right angles are formed).

Step3: Evaluate each option

• " \( \overline{OP} \) will intersect to \( \overline{QR} \)": Parallel lines don't intersect, so false.
• " \( t \) is parallel to \( \overline{OP} \)": \( t \) is perpendicular to \( \overline{OP} \), so false.
• " \( t \) is perpendicular \( \overline{OP} \) and \( \overline{QR} \)": True (right angles).
• " \( \overline{OP} \) is parallel to \( \overline{QR} \)": True (perpendicular to same line).

Answer:

• \( t \) is perpendicular \( \overline{OP} \) and \( \overline{QR} \)
• \( \overline{OP} \) is parallel to \( \overline{QR} \)