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.