To find the value of $x$, let's break down the information given:

• Line $AD$ is horizontal.
• Ray $ZC$ is vertical, extending upwards from point $Z$ on line $AD$.
• Ray $ZB$ is diagonal, extending up and to the right from point $Z$.
• Angle $AZC$ is a right angle, meaning $\angle AZC = 90^\circ$.
• $\angle CZB = 39^\circ$.
• $\angle BZD = 3x$.

From this, we can infer that the total angle around point $Z$ must sum up to $360^\circ$ because it is a full rotation. Therefore, we can set up the following equation:

$\angle AZC + \angle CZB + \angle BZD = 360^\circ$

Substituting the known values:

$90^\circ + 39^\circ + 3x = 360^\circ$

Now, solving for $x$:

$129^\circ + 3x = 360^\circ$

Subtract 129° from both sides:

$3x = 360^\circ - 129^\circ$ $3x = 231^\circ$

Now, divide by 3:

$x = \frac{231^\circ}{3} = 77^\circ$

Thus, the value of $x$ is $77^\circ$.

Would you like more details on any step, or do you have further questions?

Additional Questions:

1. How do the angles around a point always sum to 360°?
2. What is the relationship between adjacent angles when two lines intersect?
3. How do you solve for variables in geometric angle equations?
4. What is the difference between acute, right, and obtuse angles?
5. What role does the sum of angles in a triangle play in solving geometry problems?

Tip: When solving for unknown angles in geometric diagrams, always check if the angles around a point add up to 360°, or if there are other geometric properties (like supplementary or complementary angles) that can help simplify the problem.