Question

find the value of x.

Explanation:

Step1: Identify angle - relationship

The two given angles are complementary since they form a right - angle (90°). So, $(7x)^{\circ}+(2x + 9)^{\circ}=90^{\circ}$.

Step2: Combine like terms

Combine the x - terms and the constant terms: $7x+2x+9 = 90$. This simplifies to $9x+9 = 90$.

Step3: Isolate the variable term

Subtract 9 from both sides of the equation: $9x+9 - 9=90 - 9$. So, $9x=81$.

Step4: Solve for x

Divide both sides of the equation by 9: $\frac{9x}{9}=\frac{81}{9}$. Thus, $x = 9$.

Answer:

$x = 9$