Answer:
Concept:
Two angles are said to be complementary when they add up together to give 90 degrees
[tex]\begin{gathered} \angle A+\angle B=90^0 \\ \text{where,} \\ \angle A=(x+6) \\ \angle B=(7x+30)^0 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \angle A+\angle B=90^0 \\ x+6+7x+30=90^0 \\ \text{collect similar terms, we will have} \\ x+7x+6+30=90 \\ 8x+36=90 \\ \text{substract 36 from both sides} \\ 8x+36-36=90-36 \\ 8x=54 \\ \text{divide both sides by 8} \\ \frac{8x}{8}=\frac{54}{8} \\ x=6.75 \end{gathered}[/tex]To determine the value of angle A,
We will substitute the value of x= 6.75 below
[tex]\begin{gathered} A=x+6 \\ A=6.75+6 \\ A=12.75^0 \end{gathered}[/tex]Hence,
A= 12.75°
