On the card below, select which statement is incorrect.

Steps to Solve

1. Identify the Angles

The angles formed by the two intersecting lines are expressed as $3x - 100$ and $x + 50$. These can be classified as adjacent angles.

2. Set Up the Equation

Since the two angles are adjacent, we can set up the equation using the property that their measures should sum to $180^\circ$:

$$ (3x - 100) + (x + 50) = 180 $$

3. Simplify the Equation

Combine the terms on the left side:

$$ 3x - 100 + x + 50 = 180 $$

This simplifies to:

$$ 4x - 50 = 180 $$

4. Solve for x

Add $50$ to both sides to isolate the term with $x$:

$$ 4x = 230 $$

Next, divide by $4$:

$$ x = 57.5 $$

5. Evaluate Each Statement

• Statement 1: "The value of x is 75." - Incorrect, since $x = 57.5$.
• Statement 2: "The angles are corresponding angles." - Incorrect, as they are adjacent, not corresponding.
• Statement 3: "The measure of both angles is 75°." - Incorrect, as they do not both equal 75°.
• Statement 4: "We can use $3x - 100 = x + 50$ to solve for x." - This is actually incorrect since they should sum to 180, but if this is interpreted differently, note that this could also lead to contradictions.

6. Conclusion

After evaluating the statements, #1 is incorrect as the value of $x$ is actually $57.5$, not $75$.