Math Problem Statement

If l ∥ m l∥m, find the value of � x.

If l ∥ m, find the value of x.

Solution

In the given diagram, we see two parallel lines ll and mm, and a transversal intersecting them, forming two angles: one labeled as 104104^\circ and the other as (12x8)(12x - 8)^\circ.

Since lines ll and mm are parallel, the angles formed by the transversal will be either corresponding angles or alternate interior angles.

Here, the angle 104104^\circ and (12x8)(12x - 8)^\circ are alternate interior angles. For parallel lines, alternate interior angles are congruent (equal). Thus, we can set up the equation:

12x8=10412x - 8 = 104

Solving for xx:

  1. Add 8 to both sides: 12x=104+812x = 104 + 8 12x=11212x = 112

  2. Divide both sides by 12: x=11212x = \frac{112}{12} x=9.33 (or 283)x = 9.33 \ (\text{or } \frac{28}{3})

Thus, the value of xx is approximately 9.339.33 or 283\frac{28}{3}.


Would you like further details or a more in-depth explanation?

Related Questions:

  1. What are alternate interior angles in parallel lines?
  2. How can we prove that alternate interior angles are equal?
  3. What are corresponding angles, and how do they relate to parallel lines?
  4. How do you solve for unknowns in angle equations involving parallel lines?
  5. Can parallel lines and transversal angles apply to polygons? How?

Tip:

Always look for special angle relationships when you have parallel lines and a transversal. They often simplify solving for unknowns!

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Math Problem Analysis

Mathematical Concepts

Algebra
Angle Properties
Parallel Lines
Transversals

Formulas

12x - 8 = 104

Theorems

Alternate Interior Angles Theorem

Suitable Grade Level

Grades 8-10