Final answer:
Using the triangle sum theorem, where the angles of a triangle add up to 180 degrees, the correct set of angles for a triangle where the second angle is three times the first angle, and the third is the sum of the first two, is 22.5 degrees, 67.5 degrees, and 90 degrees respectively. option (A)
Step-by-step explanation:
In a triangle, the sum of the angles must always be 180 degrees. Given that the measure of the second angle is three times the measure of the first angle, and the third angle is equal to the sum of the other two angles, we can set up and solve an algebraic equation to find the correct answer. Let's denote the first angle as x, then according to the problem statement, the second angle will be 3x, and the third angle, being the sum of the first two, will be x + 3x, which simplifies to 4x.
By using the triangle sum theorem that states that the three angles in a triangle add up to 180 degrees, we can write the following equation:
x + 3x + 4x = 180
Simplifying the left side of the equation gives us 8x, which can be used to solve for x:
8x = 180
x = 180 / 8
x = 22.5
Therefore, the measures of the three angles are:
First angle: x = 22.5 degrees
Second angle: 3x = 67.5 degrees
Third angle: 4x = 90 degrees
Thus, the correct set of angles in the triangle as per the student's question is 22.5 degrees, 67.5 degrees, and 90 degrees, and among the given options, the correct one is A: x, 3x, 4x.