To complete the proof, we need to fill in the missing statements based on the given reasons. Let's go through the proof step by step.
Given:
- \( \angle 1 \) and \( \angle 2 \) are supplementary.
- \( m\angle 1 = 68^\circ \).
Prove:
- \( m\angle 2 = 112^\circ \).
Proof:
| Statements | Reasons |
|------------|---------|
| 1. \( \angle 1 \) and \( \angle 2 \) are supplementary. | 1. Given |
| 2. \( m\angle 1 + m\angle 2 = 180^\circ \) | 2. Definition of supplementary angles |
| 3. \( m\angle 1 = 68^\circ \) | 3. Given |
| 4. \( 68^\circ + m\angle 2 = 180^\circ \) | 4. Substitution Property |
| 5. \( m\angle 2 = 112^\circ \) | 5. Subtraction Property of Equality |
Explanation of Each Step:
1.
Statement 1: \( \angle 1 \) and \( \angle 2 \) are supplementary.
-
Reason: This is directly given in the problem.
2.
Statement 2: \( m\angle 1 + m\angle 2 = 180^\circ \).
-
Reason: By definition, supplementary angles are two angles whose measures add up to \( 180^\circ \).
3.
Statement 3: \( m\angle 1 = 68^\circ \).
-
Reason: This is also directly given in the problem.
4.
Statement 4: \( 68^\circ + m\angle 2 = 180^\circ \).
-
Reason: Using the Substitution Property, we substitute \( m\angle 1 = 68^\circ \) into the equation from Statement 2.
5.
Statement 5: \( m\angle 2 = 112^\circ \).
-
Reason: Using the Subtraction Property of Equality, we subtract \( 68^\circ \) from both sides of the equation \( 68^\circ + m\angle 2 = 180^\circ \):
\[
m\angle 2 = 180^\circ - 68^\circ = 112^\circ
\]
Final Answer:
\[
\boxed{
\begin{array}{|c|c|}
\hline
\text{Statements} & \text{Reasons} \\
\hline
1. \angle 1 \text{ and } \angle 2 \text{ are supplementary.} & 1. \text{Given} \\
2. m\angle 1 + m\angle 2 = 180^\circ & 2. \text{Definition of supplementary angles} \\
3. m\angle 1 = 68^\circ & 3. \text{Given} \\
4. 68^\circ + m\angle 2 = 180^\circ & 4. \text{Substitution Property} \\
5. m\angle 2 = 112^\circ & 5. \text{Subtraction Property of Equality} \\
\hline
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of two column proofs worksheet with answers.
