To solve for the value of $x$ in both parts a and b, let's analyze the two triangles.

a. Triangle with angles 25°, 22°, and x

The sum of the internal angles of a triangle is always $180^\circ$. Thus:

$x + 25^\circ + 22^\circ = 180^\circ$

Simplify:

$x + 47^\circ = 180^\circ$

Solve for $x$:

$x = 180^\circ - 47^\circ = 133^\circ$

So, $x = 133^\circ$.

b. Triangle with angles 35°, $3x$, and $(5x + 15)^\circ$

Again, the sum of the internal angles of a triangle equals $180^\circ$. Therefore:

$35^\circ + 3x + (5x + 15^\circ) = 180^\circ$

Simplify the equation:

$35^\circ + 3x + 5x + 15^\circ = 180^\circ$

Combine like terms:

$8x + 50^\circ = 180^\circ$

Solve for $8x$:

$8x = 180^\circ - 50^\circ$ $8x = 130^\circ$

Divide by 8 to find $x$:

$x = \frac{130}{8} = 16.25^\circ$

Thus, $x = 16.25^\circ$.

Final Answers:

1. a. $x = 133^\circ$
2. b. $x = 16.25^\circ$

Do you need further clarification or a step-by-step breakdown of either part?

Here are 5 related questions to explore:

1. How do we determine the sum of angles in a polygon?
2. What are exterior angles in a triangle, and how are they calculated?
3. Can the value of $x$ in a triangle ever be greater than $180^\circ$?
4. How can algebra be applied to solve problems involving triangle angles?
5. What is the significance of congruent triangles in geometry?

Tip: Always ensure that the sum of all internal angles in a triangle equals $180^\circ$. This rule helps solve for unknown angles effectively.