What is the value of \( \alpha \) ?
For the next two (02) items that follow : The equation of a straight line which passes through the origin and makes an angle \( \alpha \) (\( 0 \le \alpha \le 90^\circ \)) with the line \( L : x + \sqrt{3}y + 3\sqrt{3} = 0 \) is \( x - \sqrt{3}y = 0 \).
- A. 30^\circ
- B. 45^\circ
- C. 60^\circ ✓
- D. 90^\circ
Correct Answer: C. 60^\circ
Explanation
The slopes of the lines are 1/\sqrt{3} and -1/\sqrt{3}, corresponding to inclination angles 30^\circ and 150^\circ. The acute angle between them is 150^\circ - 30^\circ = 120^\circ, which gives an acute angle of 60^\circ.
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