Math Problem Statement

Solve for x. In the given diagram, two parallel lines (JK and LM) are intersected by a transversal (HI). The angles (3x + 25)° and (4x - 10)° are formed at the points of intersection.

Solution

In this diagram, two parallel lines (JK and LM) are intersected by a transversal (HI). The angles (3x+25)(3x + 25)^\circ and (4x10)(4x - 10)^\circ are formed at the points of intersection. Since JK and LM are parallel, we can apply the rule that corresponding angles are equal.

The angle (3x+25)(3x + 25)^\circ is corresponding to the angle (4x10)(4x - 10)^\circ, so:

3x+25=4x103x + 25 = 4x - 10

Now, let's solve for xx:

  1. Subtract 3x3x from both sides: 25=x1025 = x - 10

  2. Add 10 to both sides: 35=x35 = x

Thus, x=35x = 35.

Would you like more details or have any further questions?

Related Questions:

  1. What are alternate interior angles, and how can they be used in similar problems?
  2. How can the concept of supplementary angles be applied when working with transversals?
  3. Are there any other ways to verify if two angles are congruent in parallel line setups?
  4. What happens if the lines are not parallel but you still use transversal properties?
  5. How does solving for angles in geometry differ when working with polygons?

Tip: When solving for unknowns using angles in parallel lines, always check if the angles are corresponding, alternate interior, or supplementary to determine equality.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles
Parallel Lines
Transversals

Formulas

Corresponding Angles Theorem

Theorems

Corresponding Angles Postulate

Suitable Grade Level

Grades 8-10