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The problem states that \( \angle EGH \) is a straight angle, which means \( \angle EGH = 180^\circ \). The diagram shows two angles, \( \angle FGE = (2x - 18)^\circ \) and \( \angle FGH = (4x)^\circ \), that together form the straight angle.

To solve for \( m\angle FGH \), follow these steps:

### Step 1: Set up the equation.
Since \( \angle FGE + \angle FGH = \angle EGH = 180^\circ \), we can write the equation:

\[
(2x - 18) + 4x = 180
\]

### Step 2: Simplify the equation.
Combine like terms:

\[
6x - 18 = 180
\]

### Step 3: Solve for \( x \).
Add 18 to both sides:

\[
6x = 198
\]

Now, divide by 6:

\[
x = 33
\]

### Step 4: Find \( m\angle FGH \).
Substitute \( x = 33 \) into the expression for \( \angle FGH \):

\[
m\angle FGH = 4x = 4(33) = 132^\circ
\]

Thus, \( m\angle FGH = 132^\circ \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What would \( m\angle FGE \) be in this case?
2. How do you verify if \( \angle FGE + \angle FGH = 180^\circ \)?
3. What is the significance of a straight angle in geometry?
4. How would the problem change if \( \angle EGH \) was a different angle, say 150°?
5. How does the linear pair postulate help in solving such problems?

**Tip:** Remember that angles forming a straight line always add up to \( 180^\circ \), a key concept in solving angle-related problems.

∠EGH is a straight angle. Find m∠FGH, where ∠FGE = (2x - 18)° and ∠FGH = (4x)°.

This problem demonstrates how to solve for unknown angles on a straight line using algebra. Given ∠FGE = (2x - 18)° and ∠FGH = 4x°, learn how to calculate m∠FGH with a step-by-step solution. Suitable for students in Grades 8-10.

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