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, mnm \parallel n, crossed by a transversal. The angles formed are labeled 9595^\circ and (x+12)(x+12)^\circ.

Since lines mm and nn are parallel, the angles on the same side of the transversal are supplementary (they add up to 180180^\circ).

Thus, we can set up the following equation: 95+(x+12)=18095^\circ + (x + 12)^\circ = 180^\circ

Now, solve for xx:

95+x+12=18095 + x + 12 = 180 x+107=180x + 107 = 180 x=180107x = 180 - 107 x=73x = 73^\circ

So, the value of xx is 7373^\circ.

Would you like more details or have any questions about this? Here are some follow-up questions:

  1. What are alternate interior angles, and how do they apply here?
  2. Can you explain the concept of supplementary angles?
  3. What if the transversal formed another pair of angles—how would you find those values?
  4. What if the lines weren't parallel—how would the angle relationship change?
  5. 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