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Question

A parallelogram is shown with the diagonal drawn from the upper left vertex to the bottom right vertex. the upper left angle is 33 degrees the upper right angle is 109 degrees the bottom left is z degrees, and the bottom right is y degrees and x degrees.

Find the values of the variables x,y, and z in the parallelogram. The diagram is not drawn to scale.

Answer 1

Let's first find the value of z.

In a parallelogram, opposite angles are congruent. Since the angle in the upper left vertex is 33 degrees, the angle in the bottom right vertex must also be 33 degrees. Therefore,

z = 33 degrees.

Now, let's find the values of x and y.

The sum of the angles in a parallelogram is 360 degrees. Since we already know the angles in the upper left (33 degrees) and upper right (109 degrees) vertices, we can find the sum of the angles in the bottom left and bottom right vertices:

Angle in bottom left vertex + Angle in bottom right vertex = 360 degrees - (33 degrees + 109 degrees)
Angle in bottom left vertex + Angle in bottom right vertex = 218 degrees.

Since opposite angles in a parallelogram are congruent, the angle in the bottom left vertex must be equal to the angle in the bottom right vertex. Therefore,

2 * (Angle in bottom left vertex) = 218 degrees.

Simplifying,

Angle in bottom left vertex = 109 degrees.

Therefore,

y = x = 109 degrees. Answer: x = 109 degrees, y = 109 degrees, z = 33 degrees.