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In ΔCDE, m∠C = 26° and m∠D = 29°. Which list has the sides of ΔCDE in order from longest to shortest?

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Final answer:

To find the order of sides from longest to shortest in ΔCDE, we can determine the third angle, m∠E, by subtracting the given angles from 180°. With m∠E calculated as 125°, we order the sides opposite to angles E, D, and C, giving us the order: CE, DE, CD.

Step-by-step explanation:

The question involves determining the order of the sides of ΔCDE from longest to shortest, given the interior angles.

Since the sum of interior angles in a triangle is always 180°, we can find the third angle by subtracting the given angles from 180°:

m∠E = 180° - m∠C - m∠D = 180° - 26° - 29° = 125°

The side opposite the largest angle is the longest, and the side opposite the smallest angle is the shortest.

Hence, the sides opposite to angles E, D, and C will be ordered from longest to shortest.

So the sides will be ordered: CE (opposite to angle D), DE (opposite to angle C), and CD (opposite to angle E).

User Andy Jazz
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