Question 255943
<pre><font size = 4 color = "indigo"><b>
{{{drawing(400,400,-1,7,-4,4,

line(0,0,3cos(50*pi/180),3sin(50*pi/180)),
line(3*cos(50*pi/180),3*sin(50*pi/180),5+3*cos(50*pi/180),3*sin(50*pi/180)),
locate(2.5,0,5), locate(.6,1.3,3), locate(6.1,1.3,3), locate(4,2.7,5),
line(5+3*cos(50*pi/180),3*sin(50*pi/180),5,0), line(5,0,0,0), locate(.5,.4,"50°") 
)}}}

First we'll find this diagonal marked d.

{{{drawing(400,400,-1,7,-4,4,
line(3*cos(50*pi/180),3*sin(50*pi/180),0,0),
locate(3.4,1.6,d),
line(3*cos(50*pi/180),3*sin(50*pi/180),5+3*cos(50*pi/180),3*sin(50*pi/180)),
locate(2.5,0,5), locate(.6,1.3,3), locate(6.1,1.3,3), locate(4,2.7,5),
line(5+3*cos(50*pi/180),3*sin(50*pi/180),5,0), line(5,0,0,0), locate(.5,.4,"50°"), line(3*cos(50*pi/180),3*sin(50*pi/180),5,0) )}}}

Let's erase the upper half of the parallelogram:

{{{drawing(400,400,-1,7,-4,4,
line(3*cos(50*pi/180),3*sin(50*pi/180),0,0),
locate(3.4,1.6,d),
locate(2.5,0,5), locate(.6,1.3,3),  
 line(5,0,0,0), locate(.5,.4,"50°"), 
line(3*cos(50*pi/180),3*sin(50*pi/180),5,0) )}}}

Now we have SAS, so we use the law of cosines:

{{{d^2=3^2+5^2-2*3*5*cos("50°")}}}

{{{d^2=9+25-30cos("50°")}}}

{{{d^2=34-30(.6427876097)}}}

{{{d^2=14.71637171}}}

{{{d=3.836192345}}}

Now we go back to the original parallelogram.
Two adjacent angles of a parallelogram are
supplementary, so since 180° - 50° = 130°

{{{drawing(400,400,-1,7,-4,4,

line(0,0,3cos(50*pi/180),3sin(50*pi/180)),
line(3*cos(50*pi/180),3*sin(50*pi/180),5+3*cos(50*pi/180),3*sin(50*pi/180)),
locate(2.5,0,5), locate(.6,1.3,3), locate(6.1,1.3,3), locate(4,2.7,5),
line(5+3*cos(50*pi/180),3*sin(50*pi/180),5,0), line(5,0,0,0), locate(.5,.4,"50°"), locate(4.5,.4,"130°") 
)}}}

Next we'll find this diagonal marked d'.

{{{drawing(400,400,-1,7,-4,4,
line(3*cos(50*pi/180),3*sin(50*pi/180),0,0),
locate(3.4,1.6,"d'"),
line(3*cos(50*pi/180),3*sin(50*pi/180),5+3*cos(50*pi/180),3*sin(50*pi/180)),
locate(2.5,0,5), locate(.6,1.3,3), locate(6.1,1.3,3), locate(4,2.7,5),
line(5+3*cos(50*pi/180),3*sin(50*pi/180),5,0), line(5,0,0,0), locate(.5,.4,"50°"), line(5+3*cos(50*pi/180),3*sin(50*pi/180),0,0),
locate(4.5,.4,"130°") )}}}

Let's erase the upper half of the parallelogram:

{{{drawing(400,400,-1,7,-4,4,

locate(3.4,1.6,"d'"),

locate(2.5,0,5), locate(6.1,1.3,3), 
line(5+3*cos(50*pi/180),3*sin(50*pi/180),5,0), line(5,0,0,0), line(5+3*cos(50*pi/180),3*sin(50*pi/180),0,0),
locate(4.5,.4,"130°") )}}}

Again we have SAS, so we use the law of cosines again:

{{{"d'"^2=3^2+5^2-2*3*5*cos("130°")}}}

{{{"d'"^2=9+25-30cos("130°")}}}

{{{"d'"^2=34-30(-.6427876097)}}}

{{{"d'"^2=53.28362829}}}

{{{"d'"=7.299563569}}}

Edwin</pre>