Math Problem Statement
Solution
In this problem, you are asked to find the values of and based on the figure, where lines , meaning the two lines are parallel, and you are given the following angles:
- on the top left.
- on the bottom left.
- on the bottom right.
Step 1: Using the parallel line properties
Since , we can apply the properties of alternate interior angles and corresponding angles.
- Corresponding angles: The angle marked corresponds to the angle on the left because they are on the same side of the transversal and in corresponding positions. Therefore, we have:
Step 2: Solving for
The angles and are alternate interior angles, which are equal because the lines are parallel. Thus, we set the two angles equal:
Step 3: Solving the equation for
Now, solve the equation: Add 95 to both sides: Now divide by 6:
Final answers:
Would you like any additional details or clarification on the steps?
Here are 5 related questions for further exploration:
- What are alternate interior angles, and why are they equal when lines are parallel?
- How do corresponding angles help in solving geometry problems with parallel lines?
- How would the solution change if the lines were not parallel?
- Can you explain how vertical angles work in relation to parallel lines and a transversal?
- What are the different types of angles formed when a transversal crosses two parallel lines?
Tip: When solving geometric problems involving parallel lines, always look for alternate interior and corresponding angles, as they often provide direct relationships.
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Math Problem Analysis
Mathematical Concepts
Parallel Lines
Transversals
Corresponding Angles
Alternate Interior Angles
Formulas
x = 77° (Corresponding Angles)
6z - 95 = 77 (Alternate Interior Angles)
Theorems
Corresponding Angles Theorem
Alternate Interior Angles Theorem
Suitable Grade Level
Grades 8-10
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