Question

A and B are complementary angles. If mA=(x+8)° and mB =(8x+1),
find the measure of A

Answer 1

`\angle A=17\textdegree`

Explanation:

We know that A and B are complementary angles. So, they must add up to 90°. As an equation:

`\angle A+\angle B=90`

Since we know their equations, substitute:

`(x+8)+(8x+1)=90`

Solve for x. Combine like terms on the left:

`9x+9=90`

Subtract 9 from both sides:

`9x=81`

Divide both sides by 9:

`x=9`

So, the value of x is 9.

We want to find A. So, let's use the equation for A:

`\angle A=x+8`

Substitute 9 for x:

`\angle A=9+8`

Add:

`\angle A=17\textdegree`

So, the measure of A is 17°.