Classify the angle relationship and solve for x.
Understand the Problem
The question is asking to classify the angle relationship that pertains to the angles formed by two intersecting lines and to solve for the variable x, which is found in the expression for one of the angles.
Answer
$x = 7$
Answer for screen readers
$x = 7$
Steps to Solve
- Identify the angle relationship
The angles $(16x + 22)^\circ$ and $134^\circ$ are formed by two intersecting lines. They are vertical angles. Vertical angles are equal.
- Set up the equation
Since the angles are equal, set the expressions equal to each other:
$$ 16x + 22 = 134 $$
- Solve for x
Subtract 22 from both sides of the equation to isolate the term with x:
$$ 16x = 134 - 22 $$
Calculate the right side:
$$ 16x = 112 $$
Now, divide both sides by 16:
$$ x = \frac{112}{16} $$
Simplify the fraction:
$$ x = 7 $$
$x = 7$
More Information
Vertical angles are always equal, making it easy to set up the equation. Solving the equation leads to a straightforward calculation for $x$.
Tips
- Misidentifying angle relationships: Be careful not to confuse vertical angles with adjacent angles.
- Arithmetic errors: Double-check calculations, especially when subtracting or dividing.
AI-generated content may contain errors. Please verify critical information
