In an isosceles triangles the angles are in the ratio 7: 4: 7 Find each base angle of the triangles.

Answer

To find each base angle of the isosceles triangle with angles in the ratio 7:4:7, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**:
The angles of the triangle are given in the ratio 7:4:7. This means we can express the angles in terms of a variable \( x \):
- Let the angles be \( 7x, 4x, 7x \).

2. **Identify the Angles**:
In an isosceles triangle, two angles are equal. Here, the angles \( 7x \) are the base angles, and \( 4x \) is the vertex angle.

3. **Use the Triangle Angle Sum Property**:
The sum of the angles in any triangle is 180 degrees. Therefore, we can write the equation:
\[ 7x + 4x + 7x = 180 \]

4. **Combine Like Terms**:
Combine the terms on the left side:
\[ 18x = 180 \]

5. **Solve for \( x \)**:
Divide both sides by 18 to find \( x \):
\[ x = \frac{180}{18} = 10 \]

6. **Find Each Angle**:
Now substitute \( x \) back into the expressions for the angles:
- Base angles: \( 7x = 7 \times 10 = 70 \) degrees
- Vertex angle: \( 4x = 4 \times 10 = 40 \) degrees

7. **Conclusion**:
The base angles of the triangle are each \( 70 \) degrees, and the vertex angle is \( 40 \) degrees.

### Final Answer:
The base angles of the isosceles triangle are \( 70 \) degrees each.