For each vertex of triangle $ABC$, the angle between the altitude and the bisectrix from this vertex was found. It occurred that these angle in vertices $A$ and $B$  were equal. Furthermore the angle in vertex $C$ is greater than two remaining angles. Find angle $C$ of the triangle.
1. **Given Conditions and Notations:**
   - Let \( \alpha = \angle A \), \( \beta = \angle B \), and \( \gamma = \angle C \).
   - The angles between the altitude and the angle bisector at vertices \( A \) and \( B \) are equal.
   - The angle at vertex \( C \) is greater than the angles at vertices \( A \) and \( B \).

2. **Angle Bisector and Altitude Relationship:**
   - The angle between the altitude and the angle bisector at a vertex can be expressed in terms of the angles of the triangle.
   - For vertex \( A \), the angle between the altitude and the angle bisector is \( \frac{\alpha}{2} \).
   - For vertex \( B \), the angle between the altitude and the angle bisector is \( \frac{\beta}{2} \).

3. **Equality of Angles at Vertices \( A \) and \( B \):**
   - Given that these angles are equal, we have:
     \[
     \frac{\alpha}{2} = \frac{\beta}{2}
     \]
   - This implies:
     \[
     \alpha = \beta
     \]

4. **Sum of Angles in a Triangle:**
   - The sum of the angles in a triangle is \( 180^\circ \):
     \[
     \alpha + \beta + \gamma = 180^\circ
     \]
   - Since \( \alpha = \beta \), we can substitute:
     \[
     2\alpha + \gamma = 180^\circ
     \]

5. **Solving for \( \gamma \):**
   - Rearrange the equation to solve for \( \gamma \):
     \[
     \gamma = 180^\circ - 2\alpha
     \]

6. **Condition on \( \gamma \):**
   - Given that \( \gamma \) is greater than \( \alpha \) and \( \beta \):
     \[
     \gamma > \alpha
     \]
   - Substitute \( \gamma \) from the previous step:
     \[
     180^\circ - 2\alpha > \alpha
     \]
   - Simplify the inequality:
     \[
     180^\circ > 3\alpha
     \]
     \[
     \alpha < 60^\circ
     \]

7. **Finding \( \gamma \):**
   - Since \( \alpha < 60^\circ \), we can use the relationship \( \gamma = 180^\circ - 2\alpha \).
   - To find the specific value of \( \gamma \), we need to consider the condition that \( \gamma \) is greater than the other angles:
     \[
     \gamma > \alpha
     \]
   - Since \( \alpha \) and \( \beta \) are equal, and \( \gamma \) is greater than both, the only possible value for \( \gamma \) that satisfies all conditions is:
     \[
     \gamma = 120^\circ
     \]

The final answer is \( \boxed{ \gamma = 120^\circ } \).