Parallelogram Investigation: Analyzing a Quadrilateral with 70° and 120° Angles

In front of you the next quadrilateral:

Is it possible that it is a parallelogram?

To determine if the quadrilateral is a parallelogram, we need to verify the properties of the angles. A key property of parallelograms is that consecutive angles are supplementary, meaning their sum equals $180^\circ$.

The problem provides the measures of two consecutive angles: $\angle B = 70^\circ$ and $\angle C = 120^\circ$.

Next, let's calculate the sum of these angles:
$\angle B + \angle C = 70^\circ + 120^\circ = 190^\circ$

The sum of $\angle B$ and $\angle C$ is $190^\circ$, which is not equal to $180^\circ$.

This indicates that the quadrilateral cannot be a parallelogram because two consecutive angles do not add up to $180^\circ$.

Therefore, the given quadrilateral is not a parallelogram.
Thus, the correct answer is No.