Find the value of the variables.
options
a. x = 23, y = 134
b. x = 67, y = 46
c. x = 67, y = 134
d. x = 23, y = 46

B; since we know that angle NKL is 90° and is cut by a diagonal line that angle NKM is 67° since angles MKL and NKM both form a right angle. With this information we could now say that x is 67°, because angles NKM and LMK are alternate interior angles, stated in the alternate interior angles theorem. One of the properties of a parallelogram is that diagonal bisect each other, making all the bisected diagonal congruent, so we could use this information to find y. In the picture you could see highlighted in red the diagonals I will be focusing on. Since these two diagonals are congruent, but not the base side, this makes the shape of an isosceles triangle. We know that isosceles triangle's base angles are congruent, so we have to make label the base angles both 67°. Because of the Triangle Sum Theorem, the triangle has to equal 180°, so we add the base angles to get 134°, then we have to subtract 180° and 134° to get 46°, which is your y.