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.