 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.

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

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

\[
(7x + 26) + (4x + 29) = 180
\]

Now, combine like terms:

\[
7x + 4x + 26 + 29 = 180
\]

\[
11x + 55 = 180
\]

Next, subtract 55 from both sides:

\[
11x = 125
\]

Finally, divide both sides by 11:

\[
x = \frac{125}{11} \approx 11.36
\]

Thus, the value of \( x \) is approximately \( 11.36 \).

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 \( \angle 1 \) and \( \angle 2 \) were complementary?
4. Why is it necessary to combine like terms in equations involving variables?
5. How can we verify the calculated value of \( x \) in this context?

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

If ∠1 = (7x + 26)° and ∠2 = (4x + 29)°, then find the value of x.

Learn how to solve for x when given two supplementary angles, ∠1 = (7x + 26)° and ∠2 = (4x + 29)°. This problem demonstrates algebraic manipulation of angle relationships and the use of the supplementary angle theorem. Suitable for students in Grades 8-10.

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