In triangle ABC, `angleBAC = 75^@ , angleABC = 45^@ , bar(BC) ` is produced to D. If `angleACD` =x , then `x/3%` of `60^@` is

Options

A. `30^@`
B. `48^@`
C. `15^@`
D. `24^@`

Answer

To solve the problem, we need to find the value of \( x \) in triangle \( ABC \) where \( \angle BAC = 75^\circ \) and \( \angle ABC = 45^\circ \). Then we will calculate \( \frac{x}{3\%} \) of \( 60^\circ \).

### Step-by-Step Solution:

1. **Identify the Angles in Triangle ABC**:
- Given:
- \( \angle BAC = 75^\circ \)
- \( \angle ABC = 45^\circ \)

2. **Calculate the Third Angle \( \angle ACB \)**:
- The sum of angles in a triangle is \( 180^\circ \).
- Therefore, we can find \( \angle ACB \):
\[ \angle ACB = 180^\circ - \angle BAC - \angle ABC \]
\[ \angle ACB = 180^\circ - 75^\circ - 45^\circ \]
\[ \angle ACB = 180^\circ - 120^\circ = 60^\circ \]

3. **Determine the External Angle \( \angle ACD \)**:
- Since \( BC \) is extended to point \( D \), \( \angle ACD \) (denoted as \( x \)) is an external angle to triangle \( ABC \).
- The property of external angles states that:
\[ \angle ACD = \angle BAC + \angle ABC \]
\[ x = 75^\circ + 45^\circ \]
\[ x = 120^\circ \]

4. **Calculate \( \frac{x}{3\%} \) of \( 60^\circ \)**:
- First, we need to find \( 3\% \) of \( 60^\circ \):
\[ 3\% \text{ of } 60^\circ = \frac{3}{100} \times 60 = \frac{180}{100} = 1.8^\circ \]
- Now, we calculate \( \frac{x}{3\%} \):
\[ \frac{x}{3\%} = \frac{120^\circ}{1.8^\circ} \]
\[ = \frac{120}{1.8} = \frac{1200}{18} = \frac{200}{3} \approx 66.67 \]

5. **Final Calculation**:
- Since the question asks for \( \frac{x}{3\%} \) of \( 60^\circ \), we can also express this as:
\[ \frac{x}{3\%} = \frac{120^\circ}{1.8^\circ} \approx 66.67 \]

### Conclusion:
The answer to the question is approximately \( 66.67 \).