In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (their sum is 180°).

Step 1: Use the given angle measures

• One angle is 93°. Since consecutive angles in a parallelogram are supplementary: $93^\circ + \text{adjacent angle} = 180^\circ$ So the adjacent angle is: $180^\circ - 93^\circ = 87^\circ$

Step 2: Set up equations for the angles based on the diagram

• The angle at the top right corner is $(-2x + 3)^\circ$. This should be equal to 87° because opposite angles in a parallelogram are equal: $-2x + 3 = 87$ Solve for $x$: $-2x = 87 - 3 = 84$ $x = \frac{-84}{2} = -42$

• The angle at the bottom left corner is $(-7y + 2)^\circ$. This angle is opposite the 93° angle, so it should also be 93°: $-7y + 2 = 93$ Solve for $y$: $-7y = 93 - 2 = 91$ $y = \frac{-91}{7} = -13$

• The angle at the bottom right corner is $(-4z - 5)^\circ$. This should be equal to 87° (same as the angle opposite it): $-4z - 5 = 87$ Solve for $z$: $-4z = 87 + 5 = 92$ $z = \frac{-92}{4} = -23$

Final answers:

• $x = -42$
• $y = -13$
• $z = -23$

Would you like further details or any specific clarifications?

Here are 5 related questions for practice:

1. If one angle of a parallelogram is 110°, what are the other three angles?
2. In a parallelogram, if one angle is given as $2x$ and its consecutive angle as $3x$, find $x$.
3. How do the properties of a rectangle (a special case of a parallelogram) differ from a general parallelogram?
4. What is the sum of the interior angles of any quadrilateral, and how does it apply to a parallelogram?
5. Can a parallelogram have all four angles equal? What type of parallelogram is this?

Tip: In any parallelogram, the relationship between consecutive and opposite angles is a key property to solve for unknowns. Always remember that consecutive angles add up to 180°.