Question

angle A and angle B are complementary angles. If the measure of angle A = (9x - 3) and the measure of angle B = (10x - 2). solve for x and give the measures of both angles.

Answer 1

If two angles are complementary, their sum equals 90º

So if A and B are complementary we can say that:

$A+B=90º$

For

A=9x-3

B=10x-2

This equation is equal to

$(9x-3)+(10x-2)=90$

From this on you can solve for x:

$\begin{gathered} 9x-3+10x-2=90 \\ 9x+10x-3-2=90 \\ 19x-5=90 \\ 19x=90+5 \\ 19x=95 \\ \frac{19x}{19}=\frac{95}{19} \\ x=5 \end{gathered}$

Now that the value of x is known, replace it in the expressions for A and B to determine the measure of the angles:

$\begin{gathered} A=9x-3 \\ A=9\cdot5-3 \\ A=45-3 \\ A=42º \end{gathered}$$\begin{gathered} B=10x-2 \\ B=10\cdot5-2 \\ B=50-2 \\ B=48º \end{gathered}$

∠A=42º and ∠B=48º