Question

find m∠edc.

Explanation:

Step1: Identify the triangle type

Since \(CD = ED\), \(\triangle CDE\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. But we need to use the angle - sum property of a triangle. The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Set up the angle - sum equation

Let \(m\angle C=m\angle E = 41^{\circ}\) (if we assume the triangle is isosceles with \(CD = ED\)). Using the formula \(\angle C+\angle D+\angle E=180^{\circ}\). Substitute \(\angle C = 41^{\circ}\) and \(\angle E = 41^{\circ}\) into the equation: \(41^{\circ}+m\angle D + 41^{\circ}=180^{\circ}\).

Step3: Solve for \(m\angle D\)

Simplify the left - hand side of the equation: \(m\angle D+82^{\circ}=180^{\circ}\). Then subtract \(82^{\circ}\) from both sides: \(m\angle D=180^{\circ}- 82^{\circ}\).

Answer:

\(m\angle EDC = 98^{\circ}\)