Find the values of the variables x, y, and z in the parallelogram. the diagram is not drawn to scale.
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1- getting the value of y:
Let's take a look at the upper triangle in the parallelogram. We know that the sum of measures of a triangle is 180.The three angles forming this triangle are given as: 109°,33° and y
Therefore:
109 + 33 + y = 180
142 + y = 180
y = 180 - 142
y = 38°

2- getting the value of z:
In a parallelogram, opposite angles are congruent. Taking a look at our parallelogram, we will find that angles z and 109° are opposite.
Therefore, they are equal.
Based on the above:
z = 109°

3- getting the value of x:
Again, in a parallelogram, each two opposite sides are parallel. We also know that alternate angles formed due to parallel lines are equal. In the given parallelogram, angles 33° and x are alternate angles. This means that they are equal angles.
Therefore:
x = 33°