Question
Given that \( x+y=180, p+q=180 \), and \( p=x \). Show that \( y=q \). Which step would be used to prove the argument? A \( x+p=180 \) B \( x+y=p+q \) C \( y+q=180 \) D \( 2 x+2 y=180 \)
Ask by Wade Wagner. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
To prove that \( y = q \), the key step is:
**B \( x + y = p + q \)**
Solution
To prove that \( y = q \) given the equations \( x + y = 180 \), \( p + q = 180 \), and \( p = x \), let's analyze the steps:
1. **Given:**
\[
x + y = 180 \quad \text{(Equation 1)}
\]
\[
p + q = 180 \quad \text{(Equation 2)}
\]
\[
p = x \quad \text{(Equation 3)}
\]
2. **Substitute \( p \) from Equation 3 into Equation 2:**
\[
x + q = 180 \quad \text{(Equation 4)}
\]
3. **Now, compare Equation 1 and Equation 4:**
\[
x + y = x + q \quad \text{(Both equal to 180)}
\]
4. **Subtract \( x \) from both sides:**
\[
y = q
\]
The critical step that allows us to set up the comparison between \( x + y \) and \( x + q \) is recognizing that both \( x + y \) and \( p + q \) equal 180, and since \( p = x \), this leads directly to setting them equal to each other.
**Answer:**
**B \( x+y=p+q \)**
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Simplify this solution Bonus Knowledge
To prove that \( y = q \) given the equations \( x + y = 180 \), \( p + q = 180 \), and \( p = x \), you can start by replacing \( p \) in the second equation with \( x \). Thus, we have: \( x + q = 180 \). Now you can set the two equations equal to each other since both equal 180: \( x + y = 180 \) and \( x + q = 180 \). Now, by comparing these two equations, you can conclude that \( y = q \). The step that you would use in this argument is: **B \( x+y=p+q \)** This step allows you to equate the two sums of angles and directly leads to the conclusion that \( y = q \).
