Answer:
[tex]\angle A=17\textdegree[/tex]
Step-by-step explanation:
We know that A and B are complementary angles. So, they must add up to 90°. As an equation:
[tex]\angle A+\angle B=90[/tex]
Since we know their equations, substitute:
[tex](x+8)+(8x+1)=90[/tex]
Solve for x. Combine like terms on the left:
[tex]9x+9=90[/tex]
Subtract 9 from both sides:
[tex]9x=81[/tex]
Divide both sides by 9:
[tex]x=9[/tex]
So, the value of x is 9.
We want to find A. So, let's use the equation for A:
[tex]\angle A=x+8[/tex]
Substitute 9 for x:
[tex]\angle A=9+8[/tex]
Add:
[tex]\angle A=17\textdegree[/tex]
So, the measure of A is 17°.
