Math Problem Statement

Find x if m∠IJA = 3x − 2, m∠IJK = 128°, and m∠AJK = 11x − 10.

Solution

The problem asks to find xx, given the following angle relationships:

  • mIJA=3x2m\angle IJA = 3x - 2
  • mIJK=128m\angle IJK = 128^\circ
  • mAJK=11x10m\angle AJK = 11x - 10

By looking at the diagram, we can see that angles IJA\angle IJA, IJK\angle IJK, and AJK\angle AJK all form a straight line at point JJ, which means their sum must equal 180180^\circ. This leads to the equation:

mIJA+mAJK+mIJK=180m\angle IJA + m\angle AJK + m\angle IJK = 180^\circ

Now, substituting the given expressions:

(3x2)+(11x10)+128=180(3x - 2) + (11x - 10) + 128 = 180

Let's solve this equation step by step.

Simplifying the equation:

3x2+11x10+128=1803x - 2 + 11x - 10 + 128 = 180 Combine like terms: 14x+116=18014x + 116 = 180 Subtract 116 from both sides: 14x=6414x = 64 Divide by 14: x=6414=4.57 (rounded to two decimal places)x = \frac{64}{14} = 4.57 \text{ (rounded to two decimal places)}

Thus, x4.57x \approx 4.57.

Would you like a detailed explanation of the steps or further assistance with this?

Here are 5 questions to deepen understanding:

  1. What is the sum of angles on a straight line?
  2. How does angle addition work in linear arrangements?
  3. How do we solve linear equations when angles are expressed in terms of variables?
  4. Why is it important to combine like terms before solving for xx?
  5. What are other common types of angle problems involving straight lines?

Tip: Always double-check your algebraic work when dealing with angles and geometric figures to avoid small errors in calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Algebra
Linear Equations
Angle Addition

Formulas

Sum of angles on a straight line = 180°

Theorems

Linear Pair Theorem
Angle Addition Postulate

Suitable Grade Level

Grades 9-10