We know that
[tex]BC\perp CD[/tex]Wich means that
[tex]\angle C=90[/tex]We have an expression, in terms of x, for the values of angles A and C. Knowing the value of C, we just have to clear x from C's expression and replace it in A's:
[tex]\begin{gathered} \angle C=5x-15\rightarrow90=5x-15\rightarrow105=5x\rightarrow x=\frac{105}{5}\rightarrow x=21 \\ \text{Thus, } \\ \angle A=3x+7\rightarrow\angle A=3(21)+7\rightarrow\angle A=63+7\rightarrow\angle A=70 \end{gathered}[/tex]Hence, Angle A is worth 70°