Do/Answer (2pts): I will write out my response to the question, explaining my answer and what it means. I will explain why my answer makes sense.
Now that you have completed a proof by filling in the reasons for someone else’s statements (their work/steps), try to do a little bit of both on your own. For question 2, use your GeomA Reference sheet (posted on the Message Board/padlet), to complete the proof. (2pts)
Pro-tip: What do the two expressions make?
Given: Angles 1 and 2 are a linear pair.
Prove that x = 11
Statements
Reasons
1) Angles 1 and 2 are a linear pair.
1) Given
2) Angles 1 and 2 are supplementary.
2) Linear Pair Postulate
3) m∠1 + m∠2 = 180°
3)
4) 11x - 6 + 4x + 21 = 180
4)
5) 15x + 15 = 180
5)
6) 15x = 165
6)
7) x = 11
7)
To prove that x = 11, we start by stating that angles 1 and 2 are a linear pair. This is given information.
Next, we use the Linear Pair Postulate to conclude that angles 1 and 2 are supplementary.
Since angles 1 and 2 are supplementary, their measures must add up to 180 degrees. Therefore, we have the equation m∠1 + m∠2 = 180°.
To use this equation to solve for x, we need to write expressions for the measures of angles 1 and 2. Based on the given information, we can write the expression 11x - 6 for m∠1 and the expression 4x + 21 for m∠2.
Substituting these expressions into the equation m∠1 + m∠2 = 180°, we have (11x - 6) + (4x + 21) = 180.
By combining like terms, we simplify this equation to get 15x + 15 = 180.
We then subtract 15 from both sides to isolate the term with x. This gives us 15x = 165.
Finally, we divide both sides of the equation by 15 to solve for x, which gives us x = 11.
So, based on the given information and the algebraic steps we took, we can conclude that x = 11. This makes sense because the measures of angles 1 and 2, 11x - 6 and 4x + 21, respectively, are supplementary and add up to 180 degrees.