We can start answering this having that a rectangle is a parallelogram. The diagonals of a parallelogram bisect each other. Therefore, we have that the sides Q to the point where the diagonals intersect each other of the rectangle is congruent to R to this point. Then, we have two congruent sides.
The angles opposite to these sides are congruent too. They have the same measure. Since we have a triangle, and the sum of the internal angles of a triangle is equal to 180, we can say that:
[tex]m\angle1+2\cdot m\angle2=180[/tex]
Then, we have:
[tex]50+2\cdot m\angle2=180[/tex]
Subtracting 50 from both sides of the equation, and then dividing this equation by 2, we have:
[tex]50-50+2\cdot m\angle2_{}=180-50\Rightarrow2\cdot m\angle2=130[/tex][tex]2\cdot\frac{m\angle2}{2}=\frac{130}{2}\Rightarrow m\angle2=65[/tex]
Therefore, the measure of angle 2 (m<2) is equal to 65 (degrees) (last option).
