question
in $ \triangle c d e, m \angle c = 88 ^ { \circ } $ and $ m \angle d = 44 ^ { \circ } $. which list has the sides of $ \triangle c d e $ in order from shortest
to longest?
answer
$ \bigcirc d e, c d, e c $
$ \bigcirc e c, c d, d e $
$ \bigcirc c d, d e, e c $
$ \bigcirc e c, d e, c d $
$ \bigcirc d e, e c, c d $
$ \bigcirc c d, e c, d e $
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Question

question
in $ \triangle c d e, m \angle c = 88 ^ { \circ } $ and $ m \angle d = 44 ^ { \circ } $. which list has the sides of $ \triangle c d e $ in order from shortest
 to longest?
answer
$ \bigcirc d e, c d, e c $
$ \bigcirc e c, c d, d e $
$ \bigcirc c d, d e, e c $
$ \bigcirc e c, d e, c d $
$ \bigcirc d e, e c, c d $
$ \bigcirc c d, e c, d e $
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Accepted Answer

# Explanation:
## Step1: Find the measure of the third angle
In $\triangle CDE$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle E$ be the third angle. Then $\angle E=180^{\circ}-\angle C - \angle D$. Substituting $\angle C = 88^{\circ}$ and $\angle D=44^{\circ}$, we get $\angle E=180^{\circ}-88^{\circ}-44^{\circ}=48^{\circ}$.
## Step2: Apply the angle - side relationship
In a triangle, the side opposite the larger angle is longer. We have $\angle D = 44^{\circ}$, $\angle E=48^{\circ}$, $\angle C = 88^{\circ}$. The sides opposite these angles are $EC$ (opposite $\angle D$), $CD$ (opposite $\angle E$), and $DE$ (opposite $\angle C$) respectively. Since $44^{\circ}<48^{\circ}<88^{\circ}$, then $EC < CD<DE$ (by the angle - side relationship: if $\angle A<\angle B<\angle C$ in $\triangle ABC$, then $BC < AC<AB$).

# Answer:
EC, CD, DE

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QUESTION IMAGE

Question

Explanation:

Step1: Find the measure of the third angle

Step2: Apply the angle - side relationship

Answer: