Answer:
To solve this problem, we start by analyzing the given information and the figure described:
1. Point \( E \) is in the interior of angle \( \angle AOB \).
2. \( EC \perp OB \), meaning \( EC \) is perpendicular to \( OB \).
3. \( ED \perp OA \), meaning \( ED \) is perpendicular to \( OA \).
4. \( \angle AOB = 36^\circ \).
We need to find the measure of \( \angle CED \).
Since \( EC \perp OB \), \( EC \) forms a right angle with \( OB \). Therefore, \( \angle ECO = 90^\circ \).
Similarly, since \( ED \perp OA \), \( ED \) forms a right angle with \( OA \). Therefore, \( \angle EDO = 90^\circ \).
Since \( E \) is in the interior of \( \angle AOB \), we can find \( \angle CED \) using the fact that the angles around point \( E \) add up to \( 360^\circ \).
Let's calculate \( \angle CED \):
\[ \angle CED = 360^\circ - \angle ECO - \angle EDO \]
\[ \angle CED = 360^\circ - 90^\circ - 90^\circ \]
\[ \angle CED = 360^\circ - 180^\circ \]
\[ \angle CED = 180^\circ \]
Therefore, the measure of \( \angle CED \) is \( \boxed{180^\circ} \).
