To find the value of \( e \) given two angles \( 36^\circ \) and \( (4e)^\circ \), I will assume that the sum of these angles is equal to \( 180^\circ \) since they likely form a linear pair (they are supplementary). Let's set up the equation:
\[ 36^\circ + 4e = 180^\circ \]
Now, we can solve for \( e \).
- Subtract \( 36^\circ \) from both sides:
\[ 4e = 180^\circ - 36^\circ \] \[ 4e = 144^\circ \]
- Now, divide by 4:
\[ e = \frac{144^\circ}{4} \] \[ e = 36^\circ \]
Thus, the value of \( e \) is:
\[ \boxed{36} \]