In an isosceles triangle, if one of its equal angles is `40^(@)`, then the greatest angle is __________

Answer

To solve the problem, we need to find the greatest angle in an isosceles triangle where one of the equal angles is given as \(40^\circ\).

### Step-by-Step Solution:

1. **Understand the properties of an isosceles triangle**: In an isosceles triangle, two sides are equal, and the angles opposite those sides are also equal.

2. **Identify the angles**: Let’s denote the equal angles as \(A\) and \(A\), and the third angle as \(B\). According to the problem, we know that \(A = 40^\circ\).

3. **Set up the equation for the sum of angles**: The sum of the angles in any triangle is \(180^\circ\). Therefore, we can write the equation:
\[ A + A + B = 180^\circ \]
Substituting the value of \(A\):
\[ 40^\circ + 40^\circ + B = 180^\circ \]

4. **Simplify the equation**: Combine the equal angles:
\[ 80^\circ + B = 180^\circ \]

5. **Solve for \(B\)**: To find \(B\), subtract \(80^\circ\) from both sides:
\[ B = 180^\circ - 80^\circ = 100^\circ \]

6. **Identify the greatest angle**: Now we have the angles of the triangle as \(40^\circ\), \(40^\circ\), and \(100^\circ\). The greatest angle in the triangle is \(B\), which is \(100^\circ\).

### Final Answer:
The greatest angle is \(100^\circ\).

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