Question

which angle number represents the linear pair of ∠wyt?
diagram showing intersecting lines with angles labeled 1, 2, 3 (at x) and 4, 5, 6 (at y), with rays t, n, o, v, u, w
answer attempt 3 out of 3
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Explanation:

Step1: Recall linear pair definition

A linear pair of angles are adjacent angles that form a straight line (sum to \(180^\circ\)) and share a common side and vertex.

Step2: Identify \(\angle WYT\) and its adjacent angles

\(\angle WYT\) (angle 4) has vertex \(Y\) and sides \(YW\) and \(YT\). The adjacent angle sharing side \(YT\) and forming a straight line with \(\angle WYT\) is \(\angle UYT\) (angle 5)? Wait, no, let's check the diagram again. Wait, \(\angle WYT\) (angle 4) and \(\angle UYT\) (angle 5)? No, wait, the other side: \(\angle WYT\) (angle 4) and \(\angle VYW\) (angle 6)? No, wait, linear pair: two angles adjacent, forming a straight line. So \(\angle WYT\) (angle 4) and \(\angle UYT\) (angle 5)? Wait, no, the lines: \(TU\) and \(VW\) intersect at \(Y\). So \(\angle WYT\) (angle 4) and \(\angle UYT\) (angle 5) are adjacent? Wait, no, \(\angle WYT\) (angle 4) and \(\angle VYT\) (angle 6)? Wait, no, let's look at the angles at \(Y\). The angle \(\angle WYT\) (angle 4) and angle 5: do they form a straight line? Wait, the line \(TU\) is a straight line, so angles on a straight line at \(Y\) should be linear pairs. So \(\angle WYT\) (angle 4) and \(\angle UYT\) (angle 5) are adjacent and form a straight line? Wait, no, \(\angle WYT\) (angle 4) and angle 6? Wait, maybe I mislabel. Wait, the diagram: \(T\) and \(U\) are on a line, \(V\) and \(W\) are on another line, intersecting at \(Y\). So \(\angle WYT\) (angle 4) and \(\angle UYT\) (angle 5) are adjacent, but wait, no—wait, \(\angle WYT\) (angle 4) and \(\angle VYT\) (angle 6)? No, let's recall: linear pair must be adjacent (share a side) and their non - shared sides form a straight line. So \(\angle WYT\) (angle 4) has sides \(YW\) and \(YT\). The angle adjacent to it, sharing side \(YT\) and with non - shared side \(YU\) (so forming a straight line \(TU\)) is \(\angle UYT\) (angle 5)? Wait, no, maybe angle 6? Wait, no, let's check again. Wait, the correct linear pair for \(\angle WYT\) (angle 4) should be angle 5? Wait, no, maybe angle 6? Wait, no, let's think again. A linear pair of angles are supplementary and adjacent. So \(\angle WYT\) (angle 4) and \(\angle UYT\) (angle 5) are adjacent and their sum is \(180^\circ\) (since \(TU\) is a straight line). Wait, but also, \(\angle WYT\) (angle 4) and \(\angle VYW\) (angle 6)? No, maybe I made a mistake. Wait, the angle \(\angle WYT\) is angle 4, and the angle adjacent to it, forming a straight line, is angle 5? Wait, no, let's look at the labels: at point \(Y\), the angles are 4, 5, 6, and the other one? Wait, the diagram shows angles at \(Y\): 4, 5, 6, and maybe another? Wait, the line \(TU\) is horizontal? No, \(T\) and \(U\) are on a line, \(V\) and \(W\) on another. So \(\angle WYT\) (angle 4) and \(\angle UYT\) (angle 5) are adjacent, and \(TU\) is a straight line, so they form a linear pair. Wait, but also, \(\angle WYT\) (angle 4) and \(\angle VYT\) (angle 6)? No, angle 6 and angle 4: do they share a side? \(\angle WYT\) has side \(YW\) and \(YT\), \(\angle VYT\) has side \(YV\) and \(YT\), so they share side \(YT\), and their non - shared sides \(YW\) and \(YV\) form a straight line? Wait, \(VW\) is a straight line, so \(YV\) and \(YW\) are a straight line. So \(\angle WYT\) (angle 4) and \(\angle VYT\) (angle 6) are adjacent and form a straight line? Wait, now I'm confused. Wait, let's recall the definition again: linear pair is two adjacent angles that are supplementary (sum to \(180^\circ\)) and form a straight line. So at point \(Y\), the angles on line \(TU\) (straight line) would be \(\angle UYT\) (angle 5) and \(\angle TYW\) (angle 4)? No, wait, \(\angle UYT\) (angle 5) and \(\angle TYW\) (angle 4) share side \(YT\) and their non - shared sides \(YU\) and \(YW\) form a straight line? No, \(YU\) and \(YW\) are not a straight line. Wait, the line \(VW\) is a straight line, so angles on \(VW\) at \(Y\) are \(\angle VYW\) (angle 6) and \(\angle WYT\) (angle 4), which share side \(YW\) and their non - shared sides \(YV\) and \(YT\) form a straight line? No, \(YV\) and \(YT\) are not a straight line. Wait, I think I messed up the labels. Let's look at the diagram again: the line \(NR\) (or whatever the horizontal line is) and line \(TU\) intersect at \(X\), and line \(VW\) and \(TU\) intersect at \(Y\). So at \(Y\), the angles are: angle 4 (between \(YT\) and \(YW\)), angle 5 (between \(YU\) and \(YW\)), angle 6 (between \(YU\) and \(YV\)), and the other angle (between \(YV\) and \(YT\))? Wait, no, when two lines intersect, they form two pairs of vertical angles and four angles. Wait, line \(TU\) and line \(VW\) intersect at \(Y\), so the angles are: \(\angle TYW\) (angle 4), \(\angle WYU\) (angle 5), \(\angle UYV\) (angle 6), and \(\angle VYT\) (the fourth angle). So \(\angle TYW\) (angle 4) and \(\angle WYU\) (angle 5) are adjacent, sharing side \(YW\), and their non - shared sides \(YT\) and \(YU\) form a straight line (since \(TU\) is a straight line). So they are a linear pair. Also, \(\angle TYW\) (angle 4) and \(\angle VYT\) (the fourth angle) are vertical angles. Wait, but in the diagram, the angles at \(Y\) are labeled 4, 5, 6. Wait, maybe the fourth angle is not labeled, but among 4,5,6, the linear pair of \(\angle WYT\) (angle 4) is angle 5? Wait, no, maybe angle 6? Wait, no, let's check the sum. If \(\angle WYT\) is angle 4, and angle 5 is adjacent to it on line \(TU\), then they form a linear pair. So the linear pair of \(\angle WYT\) (angle 4) is angle 5? Wait, no, maybe I got the angle number wrong. Wait, the problem is to find the linear pair of \(\angle WYT\). Let's assume \(\angle WYT\) is angle 4. Then the linear pair should be the angle adjacent to it, forming a straight line. So if \(TU\) is a straight line, then \(\angle WYT\) (angle 4) and \(\angle UYT\) (angle 5) are adjacent and form a straight line. Wait, but also, if \(VW\) is a straight line, \(\angle WYT\) (angle 4) and \(\angle VYT\) (angle 6) are adjacent? No, angle 6 is between \(YU\) and \(YV\), angle 4 is between \(YT\) and \(YW\). So they share the vertex \(Y\) but not a common side. So the correct linear pair is angle 5? Wait, no, maybe angle 6? Wait, I think I made a mistake. Let's recall: a linear pair must share a common side and a common vertex, and their non - common sides must be opposite rays (form a straight line). So \(\angle WYT\) has sides \(YW\) and \(YT\). The angle that shares side \(YT\) and has the other side \(YV\) (so that \(YV\) and \(YW\) are opposite rays? No, \(YV\) and \(YW\) are on line \(VW\), so they are opposite rays. Wait, \(VW\) is a straight line, so \(YV\) and \(YW\) are opposite rays. So \(\angle WYT\) (sides \(YW\) and \(YT\)) and \(\angle VYT\) (sides \(YV\) and \(YT\)) share side \(YT\), and their non - shared sides \(YW\) and \(YV\) are opposite rays (form a straight line). So they are a linear pair. But in the diagram, angle 6 is \(\angle UYV\)? Wait, no, maybe the labels are: angle 4 is \(\angle WYT\), angle 5 is \(\angle WYU\), angle 6 is \(\angle UYV\). Then \(\angle WYT\) (angle 4) and \(\angle UYT\) (angle 5 + angle 6? No, no. Wait, maybe the correct answer is 5? Wait, no, let's think again. Let's look at the lines: \(TU\) is a straight line, so angles on \(TU\) at \(Y\) are \(\angle TYW\) (angle 4) and \(\angle WYU\) (angle 5), which are adjacent and form a straight line. So they are a linear pair. So the angle number is 5? Wait, but maybe I'm wrong. Wait, the other option: if \(VW\) is a straight line, then \(\angle WYT\) (angle 4) and \(\angle VYT\) (the angle between \(YV\) and \(YT\)) are a linear pair, but that angle is not labeled as 5 or 6? Wait, the diagram shows angles at \(Y\) as 4,5,6. So maybe angle 5 is \(\angle WYU\), angle 4 is \(\angle WYT\), so they share side \(YW\) and their non - shared sides \(YT\) and \(YU\) form a straight line (since \(TU\) is straight). So they are a linear pair. So the answer is 5? Wait, no, maybe 6? Wait, I'm confused. Wait, let's check the definition again. Linear pair: two angles that are adjacent (share a common side and vertex) and their non - common sides are opposite rays (form a straight line). So \(\angle WYT\) (angle 4) and \(\angle UYT\) (angle 5) share side \(YT\) (wait, no, \(\angle WYT\) has side \(YW\) and \(YT\), \(\angle UYT\) has side \(YU\) and \(YT\)? Wait, no, \(\angle UYT\) would be angle between \(YU\) and \(YT\), but in the diagram, angle 4 is between \(YT\) and \(YW\), angle 5 is between \(YW\) and \(YU\), angle 6 is between \(YU\) and \(YV\). So \(\angle WYT\) (angle 4) and \(\angle UYW\) (angle 5) share side \(YW\), and their non - shared sides \(YT\) and \(YU\) form a straight line (since \(TU\) is a straight line). So they are a linear pair. So the angle number is 5.

Answer:

5