In a triangle all the three angles A,B and C can take :

Options

A. 89
B. 90
C. 178
D. can't be determined

Answer

To solve the problem regarding the angles A, B, and C in a triangle, we need to remember the fundamental property of triangles: the sum of the interior angles of a triangle is always 180 degrees.

### Step-by-Step Solution:

1. **Understanding the Sum of Angles in a Triangle**:
In any triangle, the sum of the angles A, B, and C is given by the equation:
\[ A + B + C = 180^\circ \]

2. **Setting Limits for Each Angle**:
Each angle in a triangle must be greater than 0 degrees and less than 180 degrees. Therefore, we can express this as:
\[ 0 < A < 180, \quad 0 < B < 180, \quad 0 < C < 180 \]

3. **Finding Possible Values for Each Angle**:
Since the angles must also satisfy the equation \(A + B + C = 180^\circ\), we can deduce that:
- If angle A is very close to 180 degrees, then angles B and C must be very small, approaching 0 degrees.
- Conversely, if angle A is very small, angles B and C can be larger, but still must sum with A to equal 180 degrees.

4. **Calculating the Range of Each Angle**:
Let's consider the maximum value for angle A:
- If \(A = 178^\circ\), then \(B + C = 2^\circ\). The possible values for B and C can range from 1 degree to 1 degree each, which means:
- \(B = 1^\circ\) and \(C = 1^\circ\) (valid)
- If \(A = 1^\circ\), then \(B + C = 179^\circ\). The possible values for B and C can range from 1 degree to 178 degrees each, which means:
- \(B\) can take values from 1 to 178 degrees, and \(C\) can take values from 1 to 178 degrees.

5. **Conclusion on Possible Values**:
Therefore, the angles A, B, and C can each take values from 1 degree to 178 degrees, leading us to conclude that:
- The number of possible values for each angle is from 1 to 178, which gives us a total of 178 possible values for each angle.

### Final Answer:
Each angle A, B, and C can take values from 1 degree to 178 degrees, resulting in 178 possible values for each angle.

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