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The image asks to find the measure of angle \( \angle EFG \) in the triangle \( \triangle EFG \). The given angles and expressions are:

- \( \angle FEG = 38^\circ \)
- \( \angle EFG = 6x - 10 \)
- \( \angle FGN = 7x + 18 \)

The sum of angles in any triangle is always 180°, so the equation for the triangle \( \triangle EFG \) is:

\[
\angle FEG + \angle EFG + \angle FGN = 180^\circ
\]

Substituting the given values:

\[
38^\circ + (6x - 10) + (7x + 18) = 180^\circ
\]

Now, let's solve this equation to find the value of \( x \). Once we know \( x \), we can calculate \( m \angle EFG \).The value of \( x \) is \( \frac{134}{13} \), which is approximately \( 10.31 \).

Now, we substitute this value of \( x \) into the expression for \( \angle EFG = 6x - 10 \) to find its measure. Let’s calculate that next.The measure of \( \angle EFG \) is approximately \( 51.85^\circ \).

Since the closest option provided in the choices is 50°, the correct answer is 50°.

Would you like more details or further clarification?

Here are five related questions you might find helpful:
1. How do you find the sum of angles in a triangle?
2. Can you solve for the other angles in the triangle based on this solution?
3. How do you verify the correctness of \( x \) in this context?
4. What if the angles were in a quadrilateral—how would the process differ?
5. Can you explain how to approach other triangle problems involving unknown angles?

**Tip:** In any triangle, the sum of the interior angles will always equal 180°, which is a useful property for solving for unknown angles.

Find the measure of angle EFG in the triangle EFG, given that angle FEG = 38°, angle EFG = 6x - 10, and angle FGN = 7x + 18.

Learn how to find the measure of angle EFG in triangle EFG. This step-by-step solution involves algebraic expressions for the angles and applies the triangle angle sum theorem to solve for the unknown angle. Suitable for students in Grades 8-10.

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