To solve this problem, we will use two facts:
1.- The interior angles of a triangle add up to 180°.
2.- Vertical angles have congruent measures.
Now, using the first fact, we get that:
[tex]30^{\circ}+35^{\circ}+x=180^{\circ},[/tex]
where x is the measure of the missing angle of the bottom triangle.
Solving the above equation for x, we get:
[tex]x=180^{\circ}-30^{\circ}-35^{\circ}=115^{\circ}.[/tex]
Finally, using the second fact, we get:
[tex]m^{\circ}=115^{\circ}.[/tex]
Answer:
[tex]\begin{equation*} 115^{\circ}. \end{equation*}[/tex]
