Two parallel lines are intersected by a transversal and the two interior angles so formed on the
same side of the transversal are (2x+15°) and (3x − 20°). Then, the value of (4x +6°) is :

Question

Accepted Answer

To solve the problem, we need to understand the relationship between the angles formed when two parallel lines are intersected by a transversal. The two interior angles on the same side of the transversal are supplementary, meaning their sum is 180°.

Given angles:
1. $ (2x + 15°) $
2. $ (3x - 20°) $

According to the property of supplementary angles:
$$ (2x + 15°) + (3x - 20°) = 180° $$

Let's solve for $ x $:

$$ 2x + 15° + 3x - 20° = 180° $$
$$ 5x - 5° = 180° $$
$$ 5x = 185° $$
$$ x = 37° $$

Now, we need to find the value of $ (4x + 6°) $:

$$ 4x + 6° = 4(37°) + 6° $$
$$ = 148° + 6° $$
$$ = 154° $$

Thus, the value of $ (4x + 6°) $ is 154°, which corresponds to Option 1.

**Explanation for why each option is incorrect:**

- **Option 2 (150°):** This option is incorrect because when we substitute $ x = 37° $ into $ (4x + 6°) $, we get 154°, not 150°.
  
- **Option 3 (148°):** This option is incorrect for the same reason as above. The calculation yields 154°, not 148°.
  
- **Option 4 (146°):** This option is incorrect because the correct calculation results in 154°, not 146°.

Therefore, the correct answer is Option 1, 154°, as it accurately reflects the value of $ (4x + 6°) $ when the angles are calculated based on the given conditions.