Let's analyze the problem step by step.

Properties of a Parallelogram

1. Opposite angles are equal.
2. Adjacent angles are supplementary (sum to $180^\circ$).

Given Angles

• One angle is $79^\circ$.
• The opposite angle is $(9z - 7)^\circ$.
• Another angle is $(x + 5)^\circ$.
• The opposite angle is $(5y - 4)^\circ$.

Step 1: Solve for $z$

Since opposite angles in a parallelogram are equal: $9z - 7 = 79$ Solving for $z$:

$9z = 86$

$z = \frac{86}{9} \approx 9.56$

Step 2: Solve for $x$

Adjacent angles are supplementary:

$79 + (x + 5) = 180$

$x + 84 = 180$

$x = 96$

Step 3: Solve for $y$

Since opposite angles are equal:

$5y - 4 = x + 5$

$5y - 4 = 96 + 5$

$5y - 4 = 101$

$5y = 105$

$y = 21$

Final Answers

• $x = 96$
• $y = 21$
• $z \approx 9.56$

Would you like a step-by-step explanation of each part?

Here are some related questions to extend your understanding:

1. What other properties of a parallelogram can help solve angle problems?
2. How would the solution change if it were a rectangle instead of a parallelogram?
3. Can a parallelogram have right angles? If so, what type is it?
4. How do you calculate the sum of all interior angles in a parallelogram?
5. What are some real-life applications of parallelogram properties?

Tip:

Always check the sum of adjacent angles to ensure correctness in parallelogram problems!