In a parallelogram, opposite angles are equal, and the sum of adjacent angles is always $180^\circ$.

Let's assume that the angles of the parallelogram ABCD are as follows:

• Angle $A = x$
• Angle $B = y$
• Angle $C = x$ (since opposite angles are equal)
• Angle $D = y$ (since opposite angles are equal)

According to the problem, three of the angles are equal to two times angle $B$. This implies that:

• Angle $A = 2y$
• Angle $C = 2y$
• Angle $D = y$

Now we can set up an equation using the property that the sum of adjacent angles in a parallelogram is $180^\circ$. Let's take angles $A$ and $B$: $A + B = 180^\circ$ Substitute $A = 2y$ and $B = y$: $2y + y = 180^\circ$ $3y = 180^\circ$ $y = 60^\circ$

Now that we know $y = 60^\circ$, we can calculate the other angles:

• $A = 2y = 2 \times 60^\circ = 120^\circ$
• $C = 2y = 120^\circ$
• $D = y = 60^\circ$

Thus, the angles of the parallelogram ABCD are:

• Angle $A = 120^\circ$
• Angle $B = 60^\circ$
• Angle $C = 120^\circ$
• Angle $D = 60^\circ$

Summary:

• Angle $A = 120^\circ$
• Angle $B = 60^\circ$
• Angle $C = 120^\circ$
• Angle $D = 60^\circ$

Would you like a more detailed explanation or have any questions about this solution?

Here are some related questions:

1. How can we prove that the sum of adjacent angles in a parallelogram is always 180°?
2. What is the difference between the angles in a rhombus and a parallelogram?
3. Can a parallelogram have all angles equal? If so, what kind of parallelogram would it be?
4. How do the properties of the diagonals of a parallelogram relate to its angles?
5. What happens if one of the angles of a parallelogram is a right angle?

Tip: Always remember that in a parallelogram, opposite angles are congruent, and adjacent angles sum to $180^\circ$.