One angle of a parallelogram is twice the adjacent angle. Form the linear equations in two variables and find the measures of angles of the parallelogram. A 60 degrees, 100 degrees, 180 degrees, 20 degrees B 140 degrees, 20 degrees, 120 degrees, 80 degrees C 60 degrees, 120 degrees, 60 degrees, 120 degrees D 100 degrees, 80 degrees, 100 degrees, 80 degrees"

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The correct option is C: $$60^\circ, 120^\circ, 60^\circ, 120^\circ$$.

Let’s denote one angle of the parallelogram by $x$ and its adjacent angle by $y$. According to the problem, one angle is twice the adjacent angle, which can be expressed as: $$x = 2y \tag{1}$$

We also know that the sum of adjacent angles in a parallelogram is always $180^\circ$. Therefore, we can write: $$x + y = 180^\circ \tag{2}$$

Now, we substitute the value of $x$ from equation (1) into equation (2): $$2y + y = 180^\circ$$ $$3y = 180^\circ$$ $$\therefore y = \frac{180^\circ}{3} = 60^\circ$$

If $y = 60^\circ$, then using equation (1): $$x = 2y$$ $$x = 2(60^\circ)$$ $$x = 120^\circ$$

Thus, the measures of the angles in the parallelogram are (60^\circ) and (120^\circ). Since the angles of a parallelogram repeat, we have:

$$60^\circ, 120^\circ, 60^\circ, 120^\circ$$