Answer:
Explanation:
Let's analyze each statement and classify them as always true, sometimes true, or never true based on the figure provided:
1. m<1+m<4=180:
This statement is always true. In the figure, angles 1 and 4 are vertical angles, which means they are congruent. Therefore, m<1 = m<4, and their sum is always equal to 180 degrees.
2. m<1+m<2+m<3=180:
This statement is never true. In the figure, angles 1, 2, and 3 do not form a straight line. Therefore, the sum of m<1, m<2, and m<3 cannot be equal to 180 degrees.
3. m<2+ m<4=180:
This statement is sometimes true. In the figure, angles 2 and 4 are adjacent angles, and their sum can be equal to 180 degrees if they form a straight line. However, if angles 2 and 4 do not form a straight line, their sum will be less than 180 degrees.
4. <2=<3:
This statement is never true. In the figure, angles 2 and 3 are not congruent. Therefore, <2 is not equal to <3.
5. <2=<4:
This statement is sometimes true. In the figure, angles 2 and 4 can be congruent if they are vertical angles. However, if they are not vertical angles, they will not be congruent.
6. m<3=m<4:
This statement is always true. In the figure, angles 3 and 4 are vertical angles, which means they are congruent. Therefore, m<3 = m<4.
To summarize:
- Statement 1 is always true.
- Statement 2 is never true.
- Statement 3 is sometimes true.
- Statement 4 is never true.
- Statement 5 is sometimes true.
- Statement 6 is always true.