Question

Use the diagram shown. There are two lines which intersect each other and making angles 1 and 2. The opposite angles to 1 is 3, and 2 is 4. Which statements are true? Select all that apply. A. m∠2 + m∠3 = 180° B. m∠3 + m∠4 = 180° C. m∠2 + m∠3 = m∠3 + m∠4 D. m∠1 + m∠3 = m∠2 + m∠4

Answer 1

Answer:

I think that A, B, and C are correct.

Step-by-step explanation:

1. Since measures 2 and 3 are a linear pair, they equal 180 degrees. A is correct.

2. Since measures 3 and 4 are also a linear pair, they too equal 180 degrees. B is correct.

3. Measures 2 and 3 are already established to be 180 degrees (check answer 1) , and measures 3 and 4 are also 180 degrees (check answer 2). Since they are both 180 degrees, they are congruent (equal), so C is correct.

D is NOT correct. Measures 1 and 3 are equal because they are vertical angles. We also know that they are acute angles (less than 90) so adding them together will equal less than 180 degrees.

Measures 2 and 4 are equal because they are vertical angles, and they are obtuse (more than 90 degrees). Adding them together will equal more than 180 degrees.

Logic tells us that something less than 180 CANNOT be equal to something more than 180. This proves that 2 and 4   and   1 and 3 are not congruent.

D is WRONG