find ABCD is a parallelogram Find angle B ,C,D if angle A =50

Given that \(ABCD\) is a parallelogram and \(\angle A = 50^\circ\), we need to find the measures of the angles \(B\), \(C\), and \(D\).

### Properties of a Parallelogram:

1. **Opposite Angles are Equal:**
   - In any parallelogram, opposite angles are equal. This means:
   \[
   \angle A = \angle C \quad \text{and} \quad \angle B = \angle D.
   \]

2. **Adjacent Angles are Supplementary:**
   - Adjacent angles in a parallelogram sum up to \(180^\circ\). This implies:
   \[
   \angle A + \angle B = 180^\circ \quad \text{and} \quad \angle C + \angle D = 180^\circ.
   \]

### Step-by-step Solution:

Given that \(\angle A = 50^\circ\), we use the properties of a parallelogram to find the other angles.

1. **Find Angle \(C\):**

   Since \(\angle A\) and \(\angle C\) are opposite angles in a parallelogram, we have:
   \[
   \angle C = \angle A = 50^\circ.
   \]

2. **Find Angle \(B\) and Angle \(D\):**

   Since adjacent angles in a parallelogram are supplementary, \(\angle A + \angle B = 180^\circ\):
   \[
   \angle B = 180^\circ - \angle A.
   \]
   Substituting \(\angle A = 50^\circ\):
   \[
   \angle B = 180^\circ - 50^\circ = 130^\circ.
   \]

   Since \(\angle B\) and \(\angle D\) are opposite angles:
   \[
   \angle D = \angle B = 130^\circ.
   \]

### Summary of Angles:

- \(\angle A = 50^\circ\)
- \(\angle B = 130^\circ\)
- \(\angle C = 50^\circ\)
- \(\angle D = 130^\circ\)

Thus, the angles \(B\), \(C\), and \(D\) are \(130^\circ\), \(50^\circ\), and \(130^\circ\), respectively.

Would you like further details or have any questions?

### Related Questions:

1. What is the property of diagonals in a parallelogram?
2. How do you find the angles in a rectangle (a special type of parallelogram)?
3. If one angle of a parallelogram is \(90^\circ\), what type of parallelogram is it?
4. Can a parallelogram have all angles equal to each other?
5. What happens to the angles in a parallelogram if one side is extended?

**Tip:** Remember, in a parallelogram, opposite angles are equal, and adjacent angles add up to \(180^\circ\).

Learn how to find angles B, C, and D of parallelogram ABCD when angle A is given as 50°. Understand the properties of parallelograms where opposite angles are equal and adjacent angles are supplementary. Suitable for students in Grades 7-9.

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