1 Answer

NShiny · Answer 1 · 2021-10-09T13:43:37+0000

Answer:

$m\angle D=35.5^o$

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

$m\angle C=m\angle D$ ----> equation A

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

$m\angle C+m\angle D+m\angle E=180^o$ ----> equation B

$m\angle E=109^o$ ---> equation C

substitute equation A and equation C in equation B

$m\angle D+m\angle D+109^o=180^o\\$

$2m\angle D=180^o-109^o$

$m\angle D=35.5^o$

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