Question

Consider parallelogram VWXY below.Use the information given in the figure to find m2 Y, mZYVX, and x.W7513903xmYm ZYVY12..V

Answer 1

In a parallelogram, consecutive angles are supplementary angles.

On the other hand, since Y is supplementary to X, as well as W is supplementary to X, then Y and W have the same measure.

Additionally, since the segments WX and VY are parallel and the angles WXV and YVX are alternate interior angles, then the measure of YVX is the same as the measure of WXV.

Finally, since WV and XY are opposite sides of a parallelogram, their measures are the same. Then:

`\begin{gathered} 3x=12 \\ \Rightarrow x=4 \end{gathered}`

Therefore:

`\begin{gathered} m\angle Y=75 \\ m\angle YVX=39 \\ x=4 \end{gathered}`