To solve the given triangle problem:

The triangle has one angle marked as $31^\circ$, another as $(3x - 1)^\circ$, and a $90^\circ$ right angle. The sum of all angles in a triangle is $180^\circ$.

Using this property:

$(3x - 1) + 31 + 90 = 180$

Simplify:

$3x + 120 - 1 = 180$

$3x + 119 = 180$

Subtract 119 from both sides:

$3x = 61$

Divide by 3:

$x = \frac{61}{3} \approx 20.33$

Let me know if you want further clarification or additional details!

Here are 5 related questions for practice:

1. How do you calculate the missing angle in a triangle when two angles are known?
2. What is the importance of the angle sum property in triangle problems?
3. How can right-angle properties simplify calculations in a triangle?
4. What is the difference between acute, obtuse, and right triangles in terms of angle measures?
5. Can this method apply to non-right triangles? Why or why not?

Tip: Always verify your calculations to ensure they adhere to the geometric constraints of the problem.