Answer: The values of he variables x, y and z are
x = 33, y = 38 and z = 109.
Step-by-step explanation: Given that in the parallelogram shown, a diagonal is drawn from the upper left vertex to the bottom right vertex.
We are to find the values of the variables x, y and z in the parallelogram.
Let us name the parallelogram as ABCD as shown in the attached figure below.
Now, since ABCD is a parallelogram, so the opposite sides will be equal and parallel. Also, the opposite angles will be equal in measure.
We have
∠ABD and ∠ACD are opposite to each other.
So,
Now,
AD is parallel to BC and AC is a tranversal, so by alternate interior angles theorem, we get
Also, by angle-sum-property in triangle ACD, we have
Thus, the values of he variables x, y and z are
x = 33, y = 38 and z = 109.