Question

amath
lome
mwk 1- introduction
complete: 20%
/ line segment / ray
les
er
erpendicular, skew lines /
markings on diagrams
equations (multiplication - lz)
equations (division)
answer attempt 1 out of 2
∠
∠
submit answer
(diagram: quadrilateral yxwv with shaded angle at w)

Explanation:

Step1: Identify the shape

The figure is a rectangle (or square - like quadrilateral with right angles). In a rectangle, adjacent angles are right angles, and opposite angles are equal. Also, all angles in a rectangle are \(90^\circ\) (right angles).

Step2: Identify congruent angles

In rectangle \(VWXY\), \(\angle VWX\) (the marked angle at \(W\)) is a right angle. Other right angles in the rectangle are \(\angle WXY\), \(\angle XYV\), and \(\angle YVW\). But to find a congruent angle to \(\angle VWX\), we can look at other right angles. For example, \(\angle VWX\) and \(\angle WXY\) are both right angles (since in a rectangle, adjacent sides are perpendicular). Wait, actually, in a rectangle, all four angles are congruent (all \(90^\circ\)). So \(\angle VWX\) is congruent to \(\angle WXY\), \(\angle XYV\), and \(\angle YVW\). But let's check the vertices. The angle at \(W\) is \(\angle VWX\) (between \(VW\) and \(WX\)). Another angle congruent to it would be, for example, \(\angle WXY\) (between \(WX\) and \(XY\))? No, wait, adjacent angles in a rectangle are supplementary but also congruent (since they are \(90^\circ\)). Wait, actually, in a rectangle, all angles are equal (each \(90^\circ\)), so \(\angle VWX\cong\angle WXY\cong\angle XYV\cong\angle YVW\). But let's take the angle at \(V\): \(\angle YVW\) is also a right angle. Wait, maybe the problem is about identifying a congruent angle to \(\angle VWX\). Let's label the rectangle: vertices \(V\), \(W\), \(X\), \(Y\) in order, so \(VW\) is vertical, \(WX\) is horizontal, \(XY\) is vertical, \(YV\) is horizontal? Wait, no, the figure shows \(Y\) at the top, \(V\) at the bottom - left, \(W\) at the bottom - right, \(X\) at the top - right. So \(VW\) is a horizontal side? Wait, no, the angle at \(W\) is between \(VW\) and \(WX\). So \(VW\) and \(WX\) are adjacent sides, forming a right angle. So \(\angle VWX = 90^\circ\). Another angle with \(90^\circ\) is \(\angle WXY\) (between \(WX\) and \(XY\)), \(\angle XYV\) (between \(XY\) and \(YV\)), and \(\angle YVW\) (between \(YV\) and \(VW\)). So, for example, \(\angle VWX\) is congruent to \(\angle YVW\) (both right angles), or \(\angle WXY\), etc. But let's assume the problem is to find a congruent angle to \(\angle VWX\). Let's take \(\angle YVW\) or \(\angle WXY\) or \(\angle XYV\). But maybe the standard is to look for the angle with the same measure. Since it's a rectangle, all angles are \(90^\circ\), so any of the other three angles. Let's pick \(\angle YVW\) and \(\angle WXY\) as examples, but maybe the first one is \(\angle VWX\) and the second is \(\angle YVW\) or \(\angle WXY\). Wait, maybe the problem is to identify the angle congruent to \(\angle W\) (the marked angle). So in rectangle \(VWXY\), \(\angle W\cong\angle V\), \(\angle W\cong\angle X\), \(\angle W\cong\angle Y\)? No, wait, in a rectangle, opposite angles are equal, and adjacent angles are equal (since all are \(90^\circ\)). So all four angles are congruent. So \(\angle VWX\cong\angle WXY\cong\angle XYV\cong\angle YVW\). So possible answers: \(\angle VWX\) and \(\angle YVW\) (or any other pair). But let's go with \(\angle VWX\) and \(\angle YVW\) as a sample. Wait, maybe the problem is to name the angle congruent to \(\angle W\) (the marked angle at \(W\)). So the angle at \(W\) is \(\angle VWX\), and a congruent angle is \(\angle YVW\) (angle at \(V\)) or \(\angle WXY\) (angle at \(X\)) or \(\angle XYV\) (angle at \(Y\)).

Answer:

\(\angle VWX\) and \(\angle YVW\) (or other valid congruent angles like \(\angle WXY\), \(\angle XYV\))