The ratio of supplementary angle is 2: 3, then find the angle :

Question

Accepted Answer

To solve the problem of finding the angles with a ratio of 2:3 that are supplementary, we need to understand what supplementary angles are. Supplementary angles are two angles whose sum is 180 degrees.

Given the ratio of the angles is 2:3, let's denote the angles as 2x and 3x. According to the definition of supplementary angles:

$$ 2x + 3x = 180° $$

This simplifies to:

$$ 5x = 180° $$

To find the value of x, divide both sides by 5:

$$ x = \frac{180°}{5} = 36° $$

Now, substitute the value of x back into the expressions for the angles:

- The first angle is $ 2x = 2 \times 36° = 72° $
- The second angle is $ 3x = 3 \times 36° = 108° $

Thus, the angles are 72° and 108°, which corresponds to Option 3.

**Explanation for why other options are incorrect:**

1. **Option 1: 30°, 45°**
   - The sum of 30° and 45° is 75°, which is not equal to 180°. Therefore, these angles are not supplementary.

2. **Option 2: 36°, 54°**
   - The sum of 36° and 54° is 90°, which is not equal to 180°. Therefore, these angles are not supplementary.

3. **Option 4: 66°, 114°**
   - The sum of 66° and 114° is 180°, but the ratio of these angles is not 2:3. Therefore, this option does not satisfy the given ratio condition.

In conclusion, Option 3 is the only choice where the angles are both supplementary (sum to 180°) and maintain the given ratio of 2:3.