Find the values of the variables x, y, and z in the parallelogram. The known angles at 33 and 109

Answer

X = 33 °

Y = 38 °

Z = 109 °

Explanations

First you have to understand all properties of a parallelgram for you to answer this questions

1). Opposite sides are parallel and equal,

2). Interior opposite angles are equal.

3). If a diagonal drawn, is acts as a transvers to the opposite sides.

Solving for X

The diagonal drown makes the angle 33 to be alternate to X. Alternate angles are equal. So, X = 33o

Solving for Y

The angle 33, 109 and Y makes the angles in a triangle from the diagram. Angles in a triangle add up to 180.

33+109+Y=180

Y=180 - (33+109)

y=38°

Solving for Z

Opposite interior angles in a parallelogram are equal.

The angle 109 and Z are opposite interior angles. So Z = 109o