The vertex angle of an isosceles triangle is `80^(@)` , Find ot the measure of base angles .

Answer

To solve the problem of finding the base angles of an isosceles triangle with a vertex angle of 80 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Triangle**: We have an isosceles triangle, which we can label as triangle ABC, where angle A is the vertex angle.

2. **Given Information**: The vertex angle A is given as 80 degrees. Therefore, we have:
\[ \angle A = 80^\circ \]

3. **Understanding Isosceles Triangle Properties**: In an isosceles triangle, the two sides opposite the equal angles are of equal length. This means that angles B and C are equal:
\[ \angle B = \angle C \]

4. **Using the Angle Sum Property**: The sum of all interior angles in a triangle is always 180 degrees. Therefore, we can write the equation:
\[ \angle A + \angle B + \angle C = 180^\circ \]

5. **Substituting Known Values**: We substitute the known value of angle A into the equation:
\[ 80^\circ + \angle B + \angle C = 180^\circ \]

6. **Replacing Angles B and C**: Since \(\angle B = \angle C\), we can replace \(\angle C\) with \(\angle B\):
\[ 80^\circ + 2\angle B = 180^\circ \]

7. **Solving for Angle B**: We can now isolate \(\angle B\):
\[ 2\angle B = 180^\circ - 80^\circ \]
\[ 2\angle B = 100^\circ \]
\[ \angle B = \frac{100^\circ}{2} = 50^\circ \]

8. **Finding Angle C**: Since \(\angle B = \angle C\), we have:
\[ \angle C = 50^\circ \]

9. **Conclusion**: The measures of the base angles are:
\[ \angle B = 50^\circ \quad \text{and} \quad \angle C = 50^\circ \]

### Final Answer:
The measure of each base angle in the isosceles triangle is \(50^\circ\).

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