Math Problem Statement

If m angle, 1, equals, left parenthesis, 7, x, plus, 26, right parenthesis, degrees∠1=(7x+26) ∘ and m angle, 2, equals, left parenthesis, 4, x, plus, 29, right parenthesis, degrees∠2=(4x+29) ∘ , then find the value of x.

Solution

To solve for xx, we need to know the relationship between the angles 1\angle 1 and 2\angle 2. However, since it's not explicitly stated, let's assume that 1\angle 1 and 2\angle 2 are supplementary angles (i.e., their sum is 180 degrees).

So, the equation becomes: 1+2=180\angle 1 + \angle 2 = 180^\circ Substitute the given expressions for 1\angle 1 and 2\angle 2:

(7x+26)+(4x+29)=180(7x + 26) + (4x + 29) = 180

Now, combine like terms:

7x+4x+26+29=1807x + 4x + 26 + 29 = 180

11x+55=18011x + 55 = 180

Next, subtract 55 from both sides:

11x=12511x = 125

Finally, divide both sides by 11:

x=1251111.36x = \frac{125}{11} \approx 11.36

Thus, the value of xx is approximately 11.3611.36.

Would you like a detailed explanation of how to check the solution? Here are 5 questions to deepen your understanding:

  1. How do supplementary angles help solve problems involving angle measures?
  2. Can angles other than supplementary angles result in a similar equation?
  3. How would the solution change if 1\angle 1 and 2\angle 2 were complementary?
  4. Why is it necessary to combine like terms in equations involving variables?
  5. How can we verify the calculated value of xx in this context?

Tip: Always ensure you know the relationship between angles (e.g., complementary, supplementary) before solving.

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Math Problem Analysis

Mathematical Concepts

Algebra
Angle Relationships
Supplementary Angles

Formulas

Sum of supplementary angles: ∠1 + ∠2 = 180°

Theorems

Supplementary Angle Theorem

Suitable Grade Level

Grades 8-10