This problem involves angles in an equilateral triangle. Let’s solve for $d^\circ$ and $e^\circ$ step-by-step:

Step 1: Properties of an Equilateral Triangle

An equilateral triangle has all angles equal to $60^\circ$, and the sum of angles in a triangle is $180^\circ$.

Step 2: Label Given Angles

From the image:

• The interior angle at the vertex is split into $80^\circ$ and $e^\circ$.
• At the base of the triangle, one angle is split into $72^\circ$ and $d^\circ$, and the other is $22^\circ$.

Step 3: Solve for $e^\circ$

The angle at the top vertex of the equilateral triangle is $60^\circ$. Therefore: $80^\circ + e^\circ = 60^\circ$ $e^\circ = 60^\circ - 80^\circ = -20^\circ$

It appears there's a misinterpretation here! Let me reassess the angle relationship. Could you clarify or confirm any incorrect aspects of the can catch.details