Final answer:
Given the relationships between the angles, we find that the sum of the three angles is 265 degrees, which is greater than 180 degrees. Therefore, these angles cannot form a triangle because the sum of the interior angles of a triangle must always be 180 degrees.
Step-by-step explanation:
To determine if three angles can form a triangle, we use the fact that the sum of the interior angles of a triangle is always 180 degrees. Based on the given information, let us represent angle A as a, angle B as b, and angle C as c. We are told:
- ° is half the size of ° (b = a/2).
- The measure of ° is equal to one less than two times the measure of ° (c = 2a - 1).
- The sum of ° and ° is 114° (a + b = 114).
Now, substitute b = a/2 into a + b = 114 to find:
a + a/2 = 114
Multiplying both sides by 2 to clear the fraction:
2a + a = 228
Combine like terms:
3a = 228
Divide by 3 to solve for a:
a = 228 / 3
a = 76 degrees
Now, we find b by substituting a into b = a/2:
b = 76 / 2
b = 38 degrees
Then we find c by substituting a into c = 2a - 1:
c = 2(76) - 1
c = 152 - 1
c = 151 degrees
Last, we check if these angles can form a triangle by adding them:
a + b + c = 76 + 38 + 151
a + b + c = 265 degrees
Since the sum of angles a, b, and c is greater than 180 degrees, these angles cannot form a triangle. The concept of angles in a triangle and their sum is a fundamental topic in geometry.