Question

in a triangle with angles measuring 55°, 70°, and 55°, which of the following statements is true about the sides opposite these angles? a) the sides opposite the 55° angles are longer than the side opposite the 70° angle. b) the sides opposite the 55° angles are shorter than the side opposite the 70° angle. c) the sides opposite the 55° angles are equal in length and shorter than the side opposite the 70° angle. d) the sides opposite the 55° angles are equal in length and longer than the side opposite the 70° angle. your answer triangle def has sides de = 12 inches, ef = 9 inches, and df = 15 inches. order the angles of the triangle from smallest to largest. a) ∠d, ∠f, ∠e b) ∠e, ∠d, ∠f c) ∠f, ∠e, ∠d d) ∠e, ∠f, ∠d

Explanation:

Step1: Recall angle - side relationship in a triangle

In a triangle, the larger the angle, the longer the side opposite it. Also, if two angles are equal, the sides opposite them are equal.

Step2: Analyze the first triangle

In the triangle with angles 55°, 70°, and 55°, the two 55° angles are equal, so the sides opposite them are equal. And since 55°<70°, the sides opposite the 55° angles are shorter than the side opposite the 70° angle.

Step3: Analyze the second triangle

In triangle DEF with DE = 12 inches, EF = 9 inches, and DF = 15 inches. The smallest side is EF, the middle - length side is DE, and the longest side is DF. The angle opposite EF is ∠D, the angle opposite DE is ∠F, and the angle opposite DF is ∠E. Since the smallest side is opposite the smallest angle and the largest side is opposite the largest angle, the order of the angles from smallest to largest is ∠D, ∠F, ∠E.

Answer:

1. c) The sides opposite the 55° angles are equal in length and shorter than the side opposite the 70° angle.
2. a) ∠D, ∠F, ∠E