# In order for the parallelogram to be a square, x = [ ? ]

Mar 28, 2018

See below.

#### Explanation:

In order for a polygon to be a parallelogram, the polygon needs to be a four-sided rectangle type shape, with two sets of parallel sides.

For this square to be a parallelogram, all $4$ angles need to be 90º. This will give us to the two sets of parallel sides.

Knowing this, and the fact that on of the angles is being bisected, we need only multiply the defined angle by two and set it equal to $90$.

So we should now have something like this:

$2 \left(4 x + 17\right) = 90$

$\implies 8 x + 34 = 90$

Now all we do is solve for $x$:

$8 x + 34 = 90$

$\implies 8 x + 34 \textcolor{red}{- 34} = 90 \textcolor{red}{- 34}$

$\implies 8 x = 56$

$\implies 8 x \textcolor{red}{/ 8} = 56 \textcolor{red}{/ 8}$

$\implies x = 7$