The image shows a parallelogram with angles marked and we are tasked with finding the values of angles $a$, $b$, and $c$.

Key properties of a parallelogram:

1. Opposite angles are equal.
2. Adjacent angles are supplementary (i.e., they add up to 180°).

Given:

• One of the angles is marked as $98^\circ$.

Let's find each angle:

Step 1: Find angle $a$

• Angle $a$ is opposite the angle marked $98^\circ$, so by the property of opposite angles: $a = 98^\circ$

Step 2: Find angle $b$

• Angles $a$ and $b$ are adjacent, and adjacent angles in a parallelogram are supplementary. Therefore: $a + b = 180^\circ$ Substituting $a = 98^\circ$: $98^\circ + b = 180^\circ$ Solving for $b$: $b = 180^\circ - 98^\circ = 82^\circ$

Step 3: Find angle $c$

• Angle $c$ is opposite angle $b$, so by the property of opposite angles: $c = 82^\circ$

Final Answers:

• $a = 98^\circ$
• $b = 82^\circ$
• $c = 82^\circ$

Would you like a detailed explanation of how these properties work? Here are some related questions:

1. Why do opposite angles in a parallelogram always equal each other?
2. What other shapes have supplementary adjacent angles?
3. How can the angles in a rectangle be derived using similar rules?
4. How can we verify that the sum of all angles in any quadrilateral is always 360°?
5. What are the implications of these angle relationships for other polygons, like hexagons?

Tip: For any parallelogram, the sum of any two consecutive angles is always 180°, making supplementary angles a key concept.