To find the value of \( x \) in the isosceles triangle described, we can use the properties of triangles and the information given.
In an isosceles triangle, the angles opposite to the congruent sides are equal. Given that the angle at the vertex (where the two equal sides meet) is \( 18^\circ \), we can use the fact that the sum of all angles in a triangle is \( 180^\circ \).
Let the two equal angles be represented as \( x \). The equation can be set up as follows:
\[ x + x + 18^\circ = 180^\circ \]
This simplifies to:
\[ 2x + 18^\circ = 180^\circ \]
Subtract \( 18^\circ \) from both sides:
\[ 2x = 180^\circ - 18^\circ \]
\[ 2x = 162^\circ \]
Now, divide both sides by 2:
\[ x = \frac{162^\circ}{2} \]
\[ x = 81^\circ \]
Therefore, the value of \( x \) is \( 81^\circ \).
Final Answer: 81°