Question

solve for x.

Explanation:

Step1: Identify angle - relationship

The angles $(15x + 11)^{\circ}$ and $(5x+69)^{\circ}$ are vertical angles, and vertical angles are equal. So we set up the equation $15x + 11=5x + 69$.

Step2: Isolate x - terms

Subtract $5x$ from both sides of the equation:
$15x-5x + 11=5x-5x + 69$
$10x+11 = 69$

Step3: Isolate the constant term

Subtract 11 from both sides:
$10x+11 - 11=69 - 11$
$10x=58$

Step4: Solve for x

Divide both sides by 10:
$x=\frac{58}{10}=5.8$

Answer:

$5.8$