Geometry Problem: Find the value of X in intersecting triangles

Analyze the first triangle (on the left):
Let’s call the vertices of the first triangle (top), (bottom left), and (where the lines intersect).
The angles given in this triangle are at the top and at the bottom left.
The third angle of this triangle (at the intersection point ) can be found using the fact that the sum of angles in a triangle is :

Analyze the intersection:
The angle we just found ( ) is vertically opposite to the angle inside the second triangle (on the right) at the same intersection point. Vertically opposite angles are equal, so the angle at the intersection point inside the second triangle is also .

Analyze the second triangle (on the right):
Now we look at the triangle on the right. We know two of its interior angles:

The sum of the angles in this triangle must also be . Therefore, we can solve for :