In triangle \(ABC\), given that:

- \( \angle A - \angle B = 35^\circ \)
- \( \angle C - \angle B = 34^\circ \)

We can find the individual angles \(A\), \(B\), and \(C\) using the fact that the sum of all angles in a triangle is \(180^\circ\). Let's define the angles:

- Let \( \angle A = a \)
- Let \( \angle B = b \)
- Let \( \angle C = c \)

### Step 1: Use the relationships given
From the problem, we have two equations:
1. \( a - b = 35^\circ \) (equation 1)
2. \( c - b = 34^\circ \) (equation 2)

### Step 2: Express \( a \) and \( c \) in terms of \( b \)
From equation 1:  
\[ a = b + 35^\circ \]

From equation 2:  
\[ c = b + 34^\circ \]

### Step 3: Use the triangle angle sum property
The sum of the angles in a triangle is always \(180^\circ\), so:
\[ a + b + c = 180^\circ \]

Substitute the expressions for \( a \) and \( c \):
\[
(b + 35^\circ) + b + (b + 34^\circ) = 180^\circ
\]

### Step 4: Solve for \( b \)
Simplify the equation:
\[
3b + 69^\circ = 180^\circ
\]

Subtract \(69^\circ\) from both sides:
\[
3b = 111^\circ
\]

Now divide by 3:
\[
b = 37^\circ
\]

### Step 5: Find \( a \) and \( c \)
Using the expressions for \( a \) and \( c \):

\[
a = b + 35^\circ = 37^\circ + 35^\circ = 72^\circ
\]

\[
c = b + 34^\circ = 37^\circ + 34^\circ = 71^\circ
\]

### Final Answer:
- \( \angle A = 72^\circ \)
- \( \angle B = 37^\circ \)
- \( \angle C = 71^\circ \)

Do you have any questions or want more details? 

Here are 5 related questions for further exploration:
1. What is the relationship between the exterior angles and interior angles of a triangle?
2. How can the Law of Sines be applied to find side lengths in triangle ABC?
3. How would the result change if one of the angles were obtuse?
4. Can a triangle have two angles that differ by exactly 90 degrees? Why or why not?
5. How does the Triangle Inequality Theorem apply to this triangle?

**Tip:** Always remember that the sum of angles in any triangle is \(180^\circ\), which is essential in solving angle-based problems.

Learn how to solve for the angles of a triangle when given the difference between two of its angles. This problem uses the Triangle Angle Sum Theorem and algebraic techniques to find angle A, B, and C in a triangle ABC. Suitable for students in Grades 8-10.

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