https://file.aiquickdraw.com/mathbot/file/1728801694720zs11rg2b.jpg

The problem provided in the image is in Gujarati and involves parallel lines and angles. Here’s a breakdown of the problem:

1. **AB || CD** - Line AB is parallel to line CD.
2. **∠FGD = 5x** and **∠EFB = (120° − x)**.
3. We are asked to find the measure of **∠EFB** and **∠FGD**.

### Solution:

Given:
- ∠FGD = 5x
- ∠EFB = (120° - x)

Since AB is parallel to CD, and the angles involve corresponding or co-interior angles, we can use this information to set up an equation between these angles.

#### Step 1: Establishing a relationship between the angles

The co-interior angles in this configuration should sum to 180°. So, the sum of ∠FGD and ∠EFB should equal 180°.

\[
\text{∠FGD} + \text{∠EFB} = 180°
\]

Substitute the expressions for ∠FGD and ∠EFB:

\[
5x + (120° - x) = 180°
\]

#### Step 2: Simplifying the equation

\[
5x - x + 120° = 180°
\]
\[
4x + 120° = 180°
\]

#### Step 3: Solving for x

\[
4x = 180° - 120°
\]
\[
4x = 60°
\]
\[
x = 15°
\]

#### Step 4: Finding the values of the angles

Now that we have \(x = 15°\), we can substitute it back into the expressions for ∠FGD and ∠EFB.

- ∠FGD = 5x = \(5 \times 15° = 75°\)
- ∠EFB = 120° - x = \(120° - 15° = 105°\)

Thus, the measures of the angles are:
- **∠FGD = 75°**
- **∠EFB = 105°**

Would you like further clarification or more details on any part of this solution?

### Related Questions:
1. What is the co-interior angle theorem, and how does it apply to parallel lines?
2. How can you use algebra to solve for unknowns in geometric problems?
3. Why do the co-interior angles sum to 180° when lines are parallel?
4. What are other properties of angles formed by parallel lines and a transversal?
5. How would the problem change if the lines AB and CD were not parallel?

**Tip:** Always look for angle relationships like corresponding, alternate, or co-interior angles when working with parallel lines and transversals.

In the figure, AB || CD, ∠FGD = 5x and ∠EFB = (120° − x). Find the values of ∠EFB and ∠FGD.

This problem involves finding the values of angles ∠FGD and ∠EFB in a figure with parallel lines AB and CD. The solution uses the co-interior angle theorem, where the angles sum to 180°. Learn how to solve it step-by-step.

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