Question 1086730
<pre>
There are 4. Drawn to scale:

{{{drawing(525,400,-1,20,-8,8,

locate(3.1,0,7), locate(3.1,6,"50°"),locate(11.5,5,"50°"),locate(13.7,3.3,7),
locate(3.1,0-7,7),locate(.6,-6.3,"50°"), locate(9.6,-6.3,"50°"), 
triangle(0,0,7,0,3.5,7.505774222),locate(15.7,-3.8,7),
triangle(0+9,0,5.9465564+9,0,2.958327832+9,6.344154509),
triangle(0,0-7,7,0-7,3.5,4.171137574-7),
triangle(0+9,0-7,8.999026536+9,0-7,4.499513268+9,5.352311102-7) )}}}

BTW, If you meant EXACTLY ONE side 7 cm, not TWO sides 7 cm, and 
EXACTLY ONE angle 50°, not TWO angles 50°, then there is only 
one such isosceles triangle, the upper left one with the base 7 
and the vertex angle 50°.  The others either have TWO sides 7cm or
TWO angles 50° or both.

Edwin</pre>