In circle a shown below, marc bc is 67° and marc ef is 74°: points b, c, e, f lie on circle a. lines be and cf pass through point d creating angle edf. measure of arc bc is 67 degrees and measure of arc ef is 74 degrees. what is m∠fde? 37° 74° 70.5° 33.5°

21/58.

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when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.