We are given that ∠1 and ∠2 are supplementary, and that m∠1 = 68°. We are to prove that m∠2 = 112°.
Let’s complete the proof step by step using the provided table structure.
---
Recall:
-
Supplementary angles are two angles whose measures add up to
180°.
- The
Substitution Property allows us to replace a variable or expression with its known value.
- The
Subtraction Property of Equality says that if you subtract the same number from both sides of an equation, the equality remains true.
---
Completed Proof Table:
| Statements | Reasons |
|---------------------------------------|----------------------------------------|
| 1. ∠1 and ∠2 are supplementary | 1. Given |
| 2. m∠1 + m∠2 = 180° | 2. Definition of supplementary angles |
| 3. m∠1 = 68° | 3. Given |
| 4. 68° + m∠2 = 180° | 4. Substitution Property |
| 5. m∠2 = 112° | 5. Subtraction Property of Equality |
---
Explanation:
1.
Statement 1: We start with what is given — that ∠1 and ∠2 are supplementary. This is our starting point.
2.
Statement 2: By the *definition of supplementary angles*, the sum of their measures must be 180°. So we write:
m∠1 + m∠2 = 180°
3.
Statement 3: We’re told that
m∠1 = 68°, so we write that down as given.
4.
Statement 4: Using the *Substitution Property*, we substitute the value of m∠1 (which is 68°) into the equation from Statement 2:
→
68° + m∠2 = 180°
5.
Statement 5: Now, to solve for m∠2, we use the *Subtraction Property of Equality*: subtract 68° from both sides:
→
m∠2 = 180° - 68° = 112°
---
✔ Therefore, we have proven that
m∠2 = 112°, as required.
This is a straightforward algebraic proof based on the definition of supplementary angles and basic properties of equality.
Parent Tip: Review the logic above to help your child master the concept of geometric proof practice worksheet.
