Question

find ( mangle d ).

Explanation:

Step1: Identify triangle type

Triangle \( DEC \) is right - angled at \( E \), with \( DE = 5 \) and \( EC = 5 \). So, it is an isosceles right - triangle.

Step2: Recall angle properties of isosceles right - triangle

In an isosceles right - triangle, the two non - right angles are equal. The sum of angles in a triangle is \( 180^{\circ} \), and the right angle is \( 90^{\circ} \). Let the measure of each non - right angle be \( x \). Then \( 90^{\circ}+x + x=180^{\circ} \), which simplifies to \( 2x = 90^{\circ} \), so \( x = 45^{\circ} \). Since \( \angle D \) is a non - right angle in this isosceles right - triangle, \( m\angle D = 45^{\circ} \).

Answer:

\( 45 \)