Recall that the interior angles of a triangle add up to 180 degrees, then:
[tex]m\angle A+m\angle B+m\angle C=180^{\circ}\text{.}[/tex]Now, recall that a right angle measures 90 degrees.
Then we can set the following equation:
[tex]m\angle A+15^{\circ}+90^{\circ}=180^{\circ}.[/tex]Adding like terms we get:
[tex]m\angle A+105^{\circ}=180^{\circ}.[/tex]Subtracting 105 degrees from the above equation we get:
[tex]\begin{gathered} m\angle A+105^{\circ}-105^{\circ}=180^{\circ}-105^{\circ}, \\ m\angle A=75^{\circ}. \end{gathered}[/tex]Answer:
[tex]75.0.[/tex]