Math Problem Statement
Given two parallel lines m || n, find the value of x based on the provided angles: 95° and (x + 12)°.
Solution
In the given image, we have two parallel lines, , crossed by a transversal. The angles formed are labeled and .
Since lines and are parallel, the angles on the same side of the transversal are supplementary (they add up to ).
Thus, we can set up the following equation:
Now, solve for :
So, the value of is .
Would you like more details or have any questions about this? Here are some follow-up questions:
- What are alternate interior angles, and how do they apply here?
- Can you explain the concept of supplementary angles?
- What if the transversal formed another pair of angles—how would you find those values?
- What if the lines weren't parallel—how would the angle relationship change?
- How would this problem change if the given angle was an exterior angle?
Tip: When dealing with parallel lines and a transversal, remember that corresponding angles are equal, and consecutive interior angles are supplementary!
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Math Problem Analysis
Mathematical Concepts
Geometry
Parallel Lines
Angles
Formulas
Sum of supplementary angles = 180°
Theorems
Consecutive Interior Angles Theorem
Suitable Grade Level
Grades 8-10