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In the below figure, ABCD is a parallelogram. What is the value of x?

In the parallelogram \( ABCD \), the opposite angles are equal. The given figure shows the angles at \( \angle B \) and \( \angle D \).

Given:
- \( \angle B = 80^\circ \)
- \( \angle D = 3x + 50^\circ \)

Since \( ABCD \) is a parallelogram, the opposite angles \( \angle A \) and \( \angle C \) are also equal, and the sum of adjacent angles in a parallelogram is \( 180^\circ \). Therefore:

\[
\angle D + \angle B = 180^\circ
\]

Substituting the given values:

\[
3x + 50^\circ + 80^\circ = 180^\circ
\]

Simplifying the equation:

\[
3x + 130^\circ = 180^\circ
\]

Subtract \( 130^\circ \) from both sides:

\[
3x = 50^\circ
\]

Divide both sides by 3:

\[
x = \frac{50^\circ}{3} = 16.67^\circ
\]

Thus, the value of \( x \) is \( 16.67^\circ \).

Would you like more details or have any other questions?

Here are 5 related questions for further practice:
1. What is the measure of \( \angle D \) once \( x \) is determined?
2. How do the properties of a parallelogram help in solving for angles?
3. If \( \angle A = 70^\circ \), what is \( \angle C \) in this parallelogram?
4. How would the solution change if \( \angle B = 100^\circ \)?
5. What would be the sum of the angles \( \angle A + \angle C \)?

**Tip:** Always remember that in a parallelogram, opposite angles are equal and consecutive angles are supplementary. This property is crucial in solving angle-related problems in parallelograms.

In the figure, ABCD is a parallelogram. What is the value of x?

Explore how to calculate the value of x in a parallelogram given specific angle measurements. This problem uses core concepts in geometry, particularly the properties of parallelograms, and is ideal for students in Grades 8-10.

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