On the card below, select which statement is incorrect: #1: The angles are supplementary angles. #2: The value of x is 25. #3: The angles measure 100° and 80°. #4: We can use 3x +... On the card below, select which statement is incorrect: #1: The angles are supplementary angles. #2: The value of x is 25. #3: The angles measure 100° and 80°. #4: We can use 3x + 5 = 4x to solve for x.
Understand the Problem
The question is asking which of the four statements about the angles formed by two intersecting lines is incorrect. It provides the expressions for the angles and requires knowledge of angle relationships to identify the false statement.
Answer
The incorrect statement is #4: "We can use $3x + 5 = 4x$ to solve for $x$."
Answer for screen readers
The incorrect statement is #4: "We can use $3x + 5 = 4x$ to solve for $x$."
Steps to Solve
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Identify Angle Relationships
The angles formed by two intersecting lines are vertical angles and supplementary angles. Vertical angles are equal, and supplementary angles add up to $180^\circ$. -
Analyze Statement 1
Statement 1 claims that the angles are supplementary. Since the angles are $3x + 5$ and $4x$, they are supplementary because they add up to $180^\circ$. This statement is correct. -
Set Up the Equation
From statements 2 and 4, we need to solve for $x$ using the equation: $$ 3x + 5 + 4x = 180 $$ -
Combine Like Terms
Combine the terms in the equation: $$ 7x + 5 = 180 $$ -
Isolate $x$
Subtract 5 from both sides of the equation: $$ 7x = 175 $$ -
Solve for $x$
Now divide both sides by 7: $$ x = \frac{175}{7} = 25 $$
This confirms that statement 2 is correct. -
Find Angle Measures
Use $x = 25$ to find the angle measures:
- For the angle $3x + 5$: $$ 3(25) + 5 = 75 + 5 = 80^\circ $$
- For the angle $4x$: $$ 4(25) = 100^\circ $$
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Check Statement 3
Statement 3 claims the angles measure $100^\circ$ and $80^\circ$, which aligns with our calculations. This statement is also correct. -
Check Statement 4
Statement 4 discusses using the equation $3x + 5 = 4x$. Since this equation does not equate the two angles directly, it is incorrect to use it for their relationship.
The incorrect statement is #4: "We can use $3x + 5 = 4x$ to solve for $x$."
More Information
Statement #4 is incorrect because it misrepresents the relationship between the angles formed by the intersecting lines. The correct way to express their relationship for solving is by setting their sum equal to $180^\circ$.
Tips
- Misinterpreting vertical angles as supplementary. Remember that vertical angles are equal, while adjacent angles (like the ones formed here) are supplementary.
- Confusing angle relationships and setting up the wrong equation to solve for $x$.
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