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find x if m <FGH=125 deg, m <FGR=26x-2, and m <RGH=37x+1

Let's solve the problem using the information provided:

Given:
- \( m \angle FGH = 125^\circ \)
- \( m \angle FGR = 26x - 2 \)
- \( m \angle RGH = 37x + 1 \)

Since \( \angle FGR \) and \( \angle RGH \) are adjacent angles that sum to \( \angle FGH \), we can set up the following equation:

\[
m \angle FGR + m \angle RGH = m \angle FGH
\]

Substituting the given expressions:

\[
(26x - 2) + (37x + 1) = 125^\circ
\]

Now, combine like terms:

\[
26x + 37x - 2 + 1 = 125^\circ
\]

\[
63x - 1 = 125^\circ
\]

Add 1 to both sides:

\[
63x = 126^\circ
\]

Now, divide by 63 to solve for \( x \):

\[
x = \frac{126}{63} = 2
\]

So, the value of \( x \) is **2**.

Would you like further details on this solution or have any questions?

Here are 5 related questions to explore:
1. How can you verify the solution for \( x \) in angle problems?
2. What is the importance of adjacent angles in geometric problems?
3. How can we check if angles are correctly summed in a diagram?
4. How do equations involving angles help in solving geometric problems?
5. What are the different types of angles encountered in geometry?

**Tip:** Always substitute your solution back into the original expressions to ensure the values make sense and the conditions are satisfied.

Learn how to solve for x in a geometry problem involving angles FGH, FGR, and RGH. This problem utilizes the Adjacent Angles Theorem to find the unknown variable x. Suitable for high school students studying geometry.

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