Final answer:
The missing angles are m<1, m<2, and m<3. The only valid solution is A) m<1 = 60 degrees, m<2 = 60 degrees, m<3 = 60 degrees.
Step-by-step explanation:
The missing angles are m<1, m<2, and m<3. The given answer choices are:
- A) m<1 = 60 degrees, m<2 = 60 degrees, m<3 = 60 degrees
- B) m<1 = 90 degrees, m<2 = 45 degrees, m<3 = 45 degrees
- C) m<1 = 45 degrees, m<2 = 90 degrees, m<3 = 45 degrees
- D) m<1 = 60 degrees, m<2 = 60 degrees, m<3 = 90 degrees
We can find the missing angles by using the fact that the sum of the angles in a triangle is 180 degrees. Let's analyze each answer choice:
A) m<1 = 60 degrees, m<2 = 60 degrees, m<3 = 60 degrees: This is a valid solution because the sum of the angles is 180 degrees.
B) m<1 = 90 degrees, m<2 = 45 degrees, m<3 = 45 degrees: This is not a valid solution because the sum of the angles is 180 + 90 degrees, which is greater than 180 degrees.
C) m<1 = 45 degrees, m<2 = 90 degrees, m<3 = 45 degrees: This is not a valid solution because the sum of the angles is 45 + 90 + 45 degrees, which is greater than 180 degrees.
D) m<1 = 60 degrees, m<2 = 60 degrees, m<3 = 90 degrees: This is not a valid solution because the sum of the angles is 60 + 60 + 90 degrees, which is greater than 180 degrees.
Therefore, the only valid solution is A) m<1 = 60 degrees, m<2 = 60 degrees, m<3 = 60 degrees.