Question

Order the steps to complete the algebraic proof by putting the steps in order. (If the notation m∠P and m∠Q is confusing for you, rewrite it so m∠P = x and m∠Q =y ) Given: m∠P+m∠Q=90 , m∠Q=5m∠P Prove: m∠Q=75 (1 point) Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.

Answer 1

To solve the problem step-by-step, we will rewrite the statements using variables, as you suggested. Let's denote:

• m∠P = x
• m∠Q = y

Given:

1. \( x + y = 90 \)
2. \( y = 5x \)

Proof Steps:

1. Replace \( y \) in the first equation using the second equation:
   Substitute \( y \) with \( 5x \) in the equation \( x + y = 90 \).
   \[ x + 5x = 90 \]

2. Combine like terms:
   \[ 6x = 90 \]

3. Solve for \( x \):
   Divide both sides by 6:
   \[ x = \frac{90}{6} \]
   \[ x = 15 \]

4. Substitute \( x \) back into the equation for \( y \):
   Use \( y = 5x \):
   \[ y = 5(15) \]

5. Calculate \( y \):
   \[ y = 75 \]

Conclusion: Since \( m∠Q = y \), we have proved that \( m∠Q = 75 \).

Final Ordered Steps:

1. Substitute \( y \) with \( 5x \) in \( x + y = 90 \).
2. Combine like terms to get \( 6x = 90 \).
3. Divide both sides by 6 to find \( x = 15 \).
4. Substitute \( x \) back into \( y = 5x \).
5. Calculate \( y \) to find \( m∠Q = 75 \).

This is the correct order to follow for the algebraic proof!