Complementary angles are those angles that together add up to 90°. Therefore:
[tex](14x+5)+(19x-14)=90[/tex]And solve for x:
[tex]\begin{gathered} 14x+5+19x-14=90 \\ Add\text{ / subtract like terms} \\ 33x-9=90 \end{gathered}[/tex]Add 9 on both sides:
[tex]\begin{gathered} 33x-9+9=90+9 \\ 33x=99 \\ \text{Divide by 33} \\ \frac{33x}{33}=\frac{99}{33} \\ x=3 \end{gathered}[/tex]Next, we find the measures of the angles.
Angle 1:
[tex]14x+5=14(3)+5=42+5=47[/tex]Angle 2:
[tex]19x-14=19(3)-14=57-14=43[/tex]Answer:
Angle 1 = 47°
Angle 2 = 43°
