Question 1197065
.


            The solution by @MathLover1 is  INCORRECT.


            It is incorrect,  because she starts from wrong assumption that  " there are three right angled triangles ".


            The problem  NOWHERE  says it:  this assumption is not supported by the problem,

            so it is only in her imagination:  it is not a given fact.


            So,  I came to bring a correct solution.



<pre>
Let A be the vertex at angle "a";
    B be the vertex at angle "b",
    C be the vertex at angle "c",
    D be the vertex at angle 37°,
    P be the intersection point of the two sloped lines.


From triangle ABC, we can write equation 

    angle(A) + angle(B)  + angle(C) = 180°

or

    2a       + (180°-2b) +    c     = 180°

or

    2a - 2b  + c =  0.     (1)



Next consider triangles APC and BPD.  From these triangles, we can write equation

    a + c = b + 37°.


It is because left  side (a+c) complements angle P to 180°,
same as       right side (b+37°) complements angle P to 180°.


Last equation is equivalent to

    a - b + c = 37°.       (2)


Thus we have two equations (1) and (2)

    2a - 2b  + c =  0.     (1)
    a  -  b  + c = 37°.    (2)


Multiply equation (2) by 2;  then subtract equation (1).  You will get

    c = 2*37° = 74°.


<U>ANSWER</U>.  The measure of angle "c" is 74°.
</pre>

Solved &nbsp;(correctly).