Question

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 $60^\circ, 100^\circ, 180^\circ, 20^\circ$

B $140^\circ, 20^\circ, 120^\circ, 80^\circ$

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

D $100^\circ, 80^\circ, 100^\circ, 80^\circ"

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Answer


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:

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


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