Math Problem Statement

Solve for x in the given diagram, where two parallel lines are crossed by a transversal, forming angles 70° and 16x - 2.

Solution

To solve this problem, let’s analyze the angles given:

  1. The two parallel lines are crossed by a transversal, forming two angles: 7070^\circ and 16x216x - 2.
  2. These angles are corresponding angles, which means they are equal because the lines are parallel.

So, we set up the equation: 16x2=7016x - 2 = 70

Now, solve for xx:

  1. Add 2 to both sides: 16x=7216x = 72

  2. Divide by 16: x=7216=4.5x = \frac{72}{16} = 4.5

There’s a slight mismatch with the answer choices, which suggests either rounding or re-evaluation may be needed. However, assuming no other transformations, the closest choice would be:

None of the options provided match exactly. If rounding to a whole number, "4" would be the closest choice.

Would you like to proceed with further details, or have any other questions?


Here are 5 additional questions to expand your understanding:

  1. What are alternate interior angles, and how do they compare in parallel lines?
  2. How would you solve if the angle types were vertical angles?
  3. If the transversal were at a different angle, would the calculations change?
  4. What happens to angle measures if the lines are no longer parallel?
  5. Can you name other types of angle pairs formed by a transversal and parallel lines?

Tip: Corresponding angles are always equal when two parallel lines are cut by a transversal. Use this to check if your solution aligns with given options.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles formed by a transversal
Algebra

Formulas

Corresponding angles are equal when parallel lines are crossed by a transversal

Theorems

Corresponding Angles Postulate

Suitable Grade Level

Grades 7-10