If l and m are parallel lines and the angle on line l is 105° while the angle on line m is (3x - 18)°, what is the value of x?

Question image

Understand the Problem

The question involves determining the value of x using the properties of angles formed by two parallel lines and a transversal. Specifically, we can use the fact that these alternate interior angles sum to 180 degrees.

Answer

The value of $x$ is $31$.
Answer for screen readers

The value of $x$ is $31$.

Steps to Solve

  1. Identify Angle Relationships

Since the lines $l$ and $m$ are parallel, and the transversal creates angles, we can say that the two angles (the given $105^\circ$ and the expression $(3x - 18)^\circ$) are supplementary. This means that they add up to $180^\circ$.

  1. Set Up the Equation

Set up the equation based on the property of supplementary angles: $$ 105 + (3x - 18) = 180 $$

  1. Simplify the Equation

Combine the constant terms in the equation: $$ 105 - 18 + 3x = 180 $$

This simplifies to: $$ 87 + 3x = 180 $$

  1. Isolate the Variable

Now, isolate $3x$ by subtracting $87$ from both sides: $$ 3x = 180 - 87 $$

This simplifies to: $$ 3x = 93 $$

  1. Solve for x

Finally, divide both sides by $3$ to solve for $x$: $$ x = \frac{93}{3} = 31 $$

The value of $x$ is $31$.

More Information

This problem utilizes the properties of angles formed by two parallel lines and a transversal, specifically focusing on supplementary angles, which sum to $180^\circ$.

Tips

  • Misidentifying the angles as equal rather than supplementary. Remember that angles that are on the same side of the transversal must be added together to equal $180^\circ$.
  • Forgetting to simplify the equation correctly. Ensure to combine like terms properly to avoid errors in calculations.

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