Answer:
[tex]m\angle D=35.5^o[/tex]
Step-by-step explanation:
we know that
An isosceles triangle has two equal sides and two equal interior angles
In this problem
Triangle CDE is an isosceles triangle
because
EC ≅ DE
therefore
[tex]m\angle C=m\angle D[/tex] ----> equation A
Remember that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]m\angle C+m\angle D+m\angle E=180^o[/tex] ----> equation B
[tex]m\angle E=109^o[/tex] ---> equation C
substitute equation A and equation C in equation B
[tex]m\angle D+m\angle D+109^o=180^o\\[/tex]
[tex]2m\angle D=180^o-109^o[/tex]
[tex]m\angle D=35.5^o[/tex]
