Question

fill in a two - column proof for the following conjecture. use the reasons in the bank below, you will not use them all and can use any more than once if needed.
definition of complementary angles
definition of supplementary angles
substitution property
addition property
subtraction property
reflexive property
given
given: \\( \angle 1 \\) and \\( \angle 2 \\) are supplementary
\\( m\angle 1 = 112^{\circ} \\)
prove: \\( m\angle 2 = 68^{\circ} \\)

1. \\( \angle 1 \\) and \\( \angle 2 \\) are supplementary
2. \\( m\angle 1 = 112^{\circ} \\)
3. \\( m\angle 1 + m\angle 2 = 180^{\circ} \\)
4. \\( 112^{\circ}+m\angle 2 = 180^{\circ} \\)
5. \\( m\angle 2 = 68^{\circ} \\)

Explanation:

Step1: State the given information

1. \( \angle1\) and \( \angle2\) are supplementary - Given
2. \( m\angle1 = 112^{\circ}\) - Given

Step2: Use the definition of supplementary angles

1. \( m\angle1 + m\angle2=180^{\circ}\) - Definition of Supplementary Angles

Step3: Substitute the value of \(m\angle1\)

1. \( 112^{\circ}+m\angle2 = 180^{\circ}\) - Substitution Property

Step4: Solve for \(m\angle2\)

1. \( m\angle2=68^{\circ}\) - Subtraction Property (Subtract \(112^{\circ}\) from both sides of \(112^{\circ}+m\angle2 = 180^{\circ}\), so \(m\angle2=180^{\circ}- 112^{\circ}=68^{\circ}\))

Answer:

Statement	Reason
2. \( m\angle1 = 112^{\circ}\)	2. Given
3. \( m\angle1 + m\angle2=180^{\circ}\)	3. Definition of Supplementary Angles
4. \( 112^{\circ}+m\angle2 = 180^{\circ}\)	4. Substitution Property
5. \( m\angle2=68^{\circ}\)	5. Subtraction Property