We have that A and B are complementary, therefore their sum is equal to 90°. If ∠A and ∠B are complementary angles, this is:
[tex]\sin A=\cos B[/tex]
Where:
sin A = 4x + 10
cos B = 2x + 16
Substitute the values:
[tex]4x+10=2x+16[/tex]
And solve for x:
[tex]\begin{gathered} 4x+10-2x=2x+16-2x \\ 2x+10=16 \\ 2x+10-10=16-10 \\ 2x=6 \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}[/tex]
Answer: x = 3
