Question

parallelogram / rhombus properties, sides and angles
score: 2/5 penalty: 0.25 off
question
find the measure of the three missing angles in the parallelogram below.

Explanation:

Step1: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal. So, $x = 92$ (since $x$ is opposite to the $92^{\circ}$ angle).

Step2: Use the property of consecutive angles in a parallelogram

Consecutive angles in a parallelogram are supplementary (sum to $180^{\circ}$).
For angle $y$: $y+92 = 180$. Then $y=180 - 92=88$.

Step3: Use the property of opposite angles again

Since $z$ is opposite to $y$, $z = y$. So, $z = 88$.

Answer:

$x = 92$, $y = 88$, $z = 88$