In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the lengths of sides opposite to these angles? (2021)

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Q: In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the lengths of sides opposite to these angles? (2021)

Solution: In an isosceles triangle with angles 45 degrees, the sides opposite these angles are equal, hence the ratio is 1:1.

Steps: 6

Step 1: Identify the triangle XYZ and the given angles. We have angle X = 45 degrees and angle Y = 45 degrees.
Step 2: Recognize that in a triangle, the sum of all angles is 180 degrees. Since angle X and angle Y are both 45 degrees, we can find angle Z.
Step 3: Calculate angle Z: 180 degrees - (45 degrees + 45 degrees) = 90 degrees. So, angle Z = 90 degrees.
Step 4: Note that triangle XYZ has two angles that are equal (45 degrees each), which makes it an isosceles triangle.
Step 5: In an isosceles triangle, the sides opposite the equal angles are also equal in length.
Step 6: Since the sides opposite angle X and angle Y are equal, the ratio of their lengths is 1:1.