Question

select all the pairs of alternate exterior angles. image of intersecting lines with points p, m, l, n, q, s, r, o and angle options: ∠pqs and ∠mnl, ∠rqs and ∠mnl, ∠mnq and ∠onl, ∠pqs and ∠onl

Explanation:

To determine alternate exterior angles, we recall the definition: alternate exterior angles are formed when a transversal crosses two parallel lines (or any two lines), and they lie outside the two lines and on opposite sides of the transversal.

Step 1: Analyze ∠PQS and ∠MNL

• ∠PQS is outside the lines PQ - RQ and MN - ON, and ∠MNL is also outside, on opposite sides of the transversal SL. So this is a valid pair.

Step 2: Analyze ∠RQS and ∠MNL

• ∠RQS is inside the angle formed by PQ - RQ, so it is not an exterior angle. Thus, this pair is invalid.

Step 3: Analyze ∠MNQ and ∠ONL

• ∠MNQ and ∠ONL: ∠MNQ is outside the lines MN - ON and PQ - RQ, ∠ONL is also outside, on opposite sides of the transversal SL. This is a valid pair.

Step 4: Analyze ∠PQS and ∠ONL

• ∠PQS and ∠ONL: ∠PQS is outside, ∠ONL is outside, but they are on the same side of the transversal (not alternate). So this pair is invalid.

Answer:

The correct pairs of alternate exterior angles are:

• ∠PQS and ∠MNL
• ∠MNQ and ∠ONL

(Note: The initial selections in the image had errors. The correct pairs are identified by checking the definition of alternate exterior angles: outside the two lines, on opposite sides of the transversal.)