In the figure above, if z = 50…
When looking at the diagram, we want to start with the quadrilateral that contains angles z and y. We must remember that any quadrilateral has a total of 360 degrees. We know that two angles of the given quadrilateral are 90 degrees each and that z = 50 degrees. Thus, we can set up the following equation to determine the measure of angle y.
90 + 90 + 50 + y = 360
230 + y = 360
y = 130
Now that we know the value of angle y, we can move to the triangle in the lower part of the diagram. Let’s label it triangle ABC and draw it below. We see that angle ACB and angle y are supplementary, so angle ACB = 180 – 130 = 50 degrees. We also see that the triangle is a right triangle so the remaining angle, angle ABC = 180 – (90 + 50) = 40 degrees. Finally, since angle ABC and angle x are supplementary we see that angle x = 180 – 40 = 140 degrees.
Thus, x + y = 140 + 130 = 270.