Question

fill in the blanks to complete the two - column proof.
given: ∠1 and ∠2 are supplementary, m∠1 = 135°
prove: m∠2 = 45°
proof:

statements	reasons
2. 1	2. given
3. m∠1 + m∠2 = 180°	3. 2
4. 135°+ m∠2 = 180°	4. substitution property
5. m∠2 = 45°	5. 3

options for 1 and 2 and 3 combinations:
option 1:
1 m∠1 = 135°
2 definition of supplementary angles
3 subtraction property of equality

option 2:
1 m∠2 = 135°
2 definition of supplementary angles
3 subtraction property of equality

option 3:
1 m∠1 = 135°
2 definition of complementary angles
3 subtraction property of equality

option 4:
1 m∠1 = 135°
2 definition of supplementary angles
3 substitution property

Explanation:

Step1: Analyze Statement 2

Statement 2's reason is "Given", and from the problem, we know \( m\angle1 = 135^\circ \) is given. So [1] in Statement 2 should be \( m\angle1 = 135^\circ \).

Step2: Analyze Reason 3

Reason 3 corresponds to \( m\angle1 + m\angle2 = 180^\circ \). Supplementary angles sum to \( 180^\circ \), so the reason is "Definition of supplementary angles".

Step3: Analyze Reason 5

Reason 5 corresponds to \( m\angle2 = 45^\circ \). To get this, we subtract \( 135^\circ \) from \( 180^\circ \), which uses the "Subtraction Property of Equality".

Now, check the options: The first option has [1] \( m\angle1 = 135^\circ \), [2] Definition of supplementary angles, [3] Subtraction Property of Equality, which matches our analysis.

Answer:

The correct option is:
[1] \( m\angle1 = 135^\circ \)
[2] Definition of supplementary angles
[3] Subtraction Property of Equality (the first option among the choices)