What is x if (x + 6)° and (3x - 2)° relate to a 34° angle?
Understand the Problem
The question involves solving for the variable x in a geometry problem where angles are given in terms of x. The angles (x + 6)° and (3x - 2)° are related to the angle of 34°, likely involving angle relationships such as vertical angles or supplementary angles.
Answer
The value of \( x \) is \( 7.5 \).
Answer for screen readers
The value of $x$ is ( x = 7.5 ).
Steps to Solve
- Determine Angle Relationships
Given the angles $(x + 6)^\circ$ and $(3x - 2)^\circ$, we need to relate them to the angle of $34^\circ$. These angles can be equal to $34^\circ$ or supplementary to it. We will assume they are supplementary: $$ (x + 6) + (3x - 2) = 34 $$
- Combine Like Terms
Combine the terms from the left side of the equation: $$ x + 6 + 3x - 2 = 34 $$ This simplifies to: $$ 4x + 4 = 34 $$
- Isolate the Variable
Next, solve for $x$ by first subtracting $4$ from both sides: $$ 4x = 30 $$ Now, divide by $4$: $$ x = \frac{30}{4} $$
- Simplify the Solution
Simplifying the fraction gives: $$ x = 7.5 $$
The value of $x$ is ( x = 7.5 ).
More Information
The angles in the problem are directly related to simple geometry concepts. The solution involves understanding angle relationships, where supplementary angles add up to $180^\circ$ and can help derive the value of a variable in expressions representing angles.
Tips
- Ignoring the relationship: Sometimes students might forget to consider that the angles could be supplementary or wrongly assume they are equal.
- Miscalculating when combining like terms: Ensure you carefully combine the $x$ terms and constant terms without errors.
- Failing to simplify the final answer correctly: Always check if your final numerical answer can be simplified further.
AI-generated content may contain errors. Please verify critical information
