I think your teacher may have made a typo. Refer to the diagram below. If we ignore segment ZA for now, we can see a rectangle forms with angle W = angle Y = 90. Also, we can see that WX = 6 is the horizontal base and WZ = 8 is the vertical height.
However, the side opposite WZ (which is XY) should also be 8 cm tall, and not 6 cm. If XY was 6 cm, then point Y would move to where point A is located (and the quadrilateral would be WXAZ instead of WXYZ). This new quadrilateral would not have a 90 degree angle at point Y's new location.
In other words, if we want angle Y to be 90 degrees, then side XY must be 8 units long. I have a feeling this is where the typo is, but your teacher might have been intending to say something else.
Two triangles are similar if they have:
<span>all their angles equalcorresponding sides are in the same ratio</span>
But we don't need to know all three sides and all three angles ...two or three out of the six is usually enough.
There are three ways to find if two triangles are similar: AA, SAS and SSS:
These triangles are congruent by AAS condition hence the statement is true
Since a straight line is 180 degrees, if you subtract 180-48 you get 132. Divide this by 2 and get X= 66. Because all angle of a triangle add up to 180, subtract the 90 from the right angle and 66 from x from 180. 180-66-90= 24. This means z=24