Final Answer:
The longest side is opposite angle A, which measures 125 degrees.
The middle-length side is opposite angle B, which measures 55 degrees.
The shortest side is opposite angle C, which measures 26 degrees.
Step-by-step explanation:
To solve the problem, we are given that the angles in triangle ABC are related to a variable x as follows:
Angle A = 10x - 5
Angle B = 5x - 10
Angle C = 52 - 2x
To find the value of x, we will use the property that the sum of the angles in any triangle is 180 degrees. Hence, we have:
Angle A + Angle B + Angle C = 180
Substitute the given expressions for angles A, B, and C:
(10x - 5) + (5x - 10) + (52 - 2x) = 180
Combine like terms:
10x + 5x - 2x = 180 + 5 + 10 - 52
13x - 2x = 143
11x = 143
Divide by 11 to solve for x:
x = 143 / 11
x = 13
Now that we have the value of x, we can calculate the measures of the angles:
Angle A = 10x - 5 = 10(13) - 5 = 130 - 5 = 125 degrees
Angle B = 5x - 10 = 5(13) - 10 = 65 - 10 = 55 degrees
Angle C = 52 - 2x = 52 - 2(13) = 52 - 26 = 26 degrees
Therefore, the sides of triangle ABC, listed from shortest to longest, are opposite the angles in the order: C, B, A.
Complete question:
Angle A = 10x-5, Angle B = 5x - 10, and Angle C = 52 - 2x. List the sides of ABC in order from shortest to longest.