Question

select all angles that are corresponding to $\angle 3$.
$\angle 1$ $\angle 4$ $\angle 5$ $\angle 6$

Explanation:

Step1: Recall Corresponding Angles

Corresponding angles are in the same relative position at each intersection where a transversal crosses parallel lines.

Step2: Analyze ∠3's Position

∠3 is at the upper - left intersection of the transversal and the first parallel line. We check the other intersection (with the second parallel line). The angle in the same relative position (upper - left) is ∠5? Wait, no, wait. Wait, the transversal and the two parallel lines: ∠3 is formed by the horizontal line (transversal?) Wait, no, the two horizontal lines are parallel, and the two slanted lines are transversals? Wait, no, looking at the diagram: the first intersection has angles 3,2,8,7; the second has 5,6,1,4. The transversal is the slanted line? Wait, no, the horizontal line is the transversal? Wait, no, the two slanted lines are the same (parallel?) Wait, no, the two slanted lines are parallel? Wait, the problem is about corresponding angles. Corresponding angles: when two parallel lines are cut by a transversal, corresponding angles are equal. So ∠3: let's see the position. ∠3 is above the horizontal line (the transversal?) and to the left of the slanted line (the other line). At the second intersection, above the horizontal line and to the left of the slanted line is ∠5? Wait, no, wait the options: ∠1, ∠4, ∠5, ∠6. Wait, maybe I got the lines wrong. Let's re - examine: the two horizontal lines are parallel, and the slanted line is the transversal. So ∠3 and ∠5: no, wait ∠3 is at the first intersection (left circle), ∠5 is at the second (right circle). Wait, the correct corresponding angle: when the transversal (slanted line) cuts the two parallel horizontal lines, ∠3 and ∠5? No, wait ∠3 is in the upper - left of its intersection, ∠5 is in the upper - left of its intersection? Wait, no, maybe the horizontal line is the transversal. Wait, no, the standard corresponding angles: if we have two parallel lines (the slanted ones) cut by a transversal (the horizontal one). Then ∠3 and ∠5: no, ∠3 is at the top - left of the first intersection (between horizontal and slanted), ∠5 is at the top - left of the second intersection (between horizontal and slanted). Wait, but let's check the options. Wait, maybe I made a mistake. Wait, the correct corresponding angle to ∠3 is ∠5? No, wait the options include ∠5. Wait, no, wait the diagram: ∠3 is above the horizontal line and to the left of the slanted line. At the second intersection (right circle), above the horizontal line and to the left of the slanted line is ∠5. Wait, but let's confirm. Corresponding angles: same position relative to the parallel lines and the transversal. So ∠3 and ∠5: yes? Wait, no, wait the other angles. Wait, maybe the transversal is the slanted line, and the two horizontal lines are parallel. Then ∠3 and ∠5: no, ∠3 is on the first horizontal line (top) and left of the slanted line, ∠5 is on the second horizontal line (top) and left of the slanted line. So they are corresponding angles. Wait, but let's check the options. The options are ∠1, ∠4, ∠5, ∠6. Wait, maybe I was wrong. Wait, no, let's think again. ∠3: the angle ∠3 and ∠5: are they corresponding? Wait, maybe the correct answer is ∠5? Wait, no, wait the user's diagram: let's see the angles. ∠3 is at the upper left of the first intersection, ∠5 is at the upper left of the second intersection. So ∠3 and ∠5 are corresponding angles. Wait, but let's check the options. Wait, maybe I made a mistake. Wait, no, the correct corresponding angle to ∠3 is ∠5? Wait, no, wait the answer: among the options, ∠5 is the corresponding angle? Wait, no, wait the problem says "select all angles". Wait, maybe I messed up the lines. Let's start over. Corresponding angles: when two parallel lines are cut by a transversal, corresponding angles are in the same "corner". So ∠3: let's identify the lines. The two horizontal lines are parallel, and the slanted line is the transversal. So ∠3 is formed by the horizontal line (below) and the slanted line (left), above the horizontal line? Wait, no, the first intersection: angles 3 (top - left), 2 (top - right), 8 (bottom - right), 7 (bottom - left). The second intersection: 5 (top - left), 6 (top - right), 1 (bottom - left), 4 (bottom - right). So if the two horizontal lines are parallel and the slanted line is the transversal, then ∠3 (top - left) and ∠5 (top - left) are corresponding angles. So the angle corresponding to ∠3 is ∠5. Wait, but the options are ∠1, ∠4, ∠5, ∠6. So we check: ∠3 and ∠5 are corresponding.

Answer:

$\angle5$ (Wait, but let's confirm again. Wait, maybe the transversal is the horizontal line, and the two slanted lines are parallel. Then ∠3 and ∠5: no, ∠3 is at the intersection of the horizontal line and the first slanted line, ∠5 is at the intersection of the horizontal line and the second slanted line. If the two slanted lines are parallel, then ∠3 and ∠5 are corresponding angles. So the answer is ∠5. So we select ∠5.