In `DeltaABC,angleA=angleC=50^(@)` .the longest side of `DeltaABC` is ______ .

Answer

To solve the problem, we need to determine the longest side of triangle ABC given that angle A and angle C are both 50 degrees.

### Step-by-Step Solution:

1. **Identify the Given Angles**:
We know that angle A = 50° and angle C = 50°.

2. **Use the Triangle Sum Property**:
The sum of the angles in a triangle is always 180°. Therefore, we can find angle B using the formula:
\[ \text{Angle B} = 180° - \text{Angle A} - \text{Angle C} \]
Substituting the known values:
\[ \text{Angle B} = 180° - 50° - 50° = 80° \]

3. **Identify the Largest Angle**:
Now we have the angles:
- Angle A = 50°
- Angle B = 80°
- Angle C = 50°

The largest angle among these is angle B, which is 80°.

4. **Use the Property of Angles and Sides**:
According to the property of triangles, the longest side is opposite the largest angle. Since angle B is the largest angle, the longest side will be opposite to angle B.

5. **Determine the Longest Side**:
The side opposite to angle B (which is the largest angle) is side AC. Therefore, side AC is the longest side of triangle ABC.

### Final Answer:
The longest side of triangle ABC is **side AC**.

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