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 , we need to know the relationship between the angles and . However, since it's not explicitly stated, let's assume that and are supplementary angles (i.e., their sum is 180 degrees).
So, the equation becomes: Substitute the given expressions for and :
Now, combine like terms:
Next, subtract 55 from both sides:
Finally, divide both sides by 11:
Thus, the value of is approximately .
Would you like a detailed explanation of how to check the solution? Here are 5 questions to deepen your understanding:
- How do supplementary angles help solve problems involving angle measures?
- Can angles other than supplementary angles result in a similar equation?
- How would the solution change if and were complementary?
- Why is it necessary to combine like terms in equations involving variables?
- How can we verify the calculated value of 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
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