Question

Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above. The value of \( \theta \), in degrees, is 

• A. 36
• B. 45
• C. 72
• D. 108

Hint:

When a star is formed with equal-length line segments, divide the total angle of a circle (360°) by the number of line segments to find the angle at each intersection.

Answer 1

The Correct Option is A

The star is formed using five equal line segments. The angles formed between these lines at the center of the star are crucial. We can recognize that the angles between two consecutive segments form an angle \( \theta \). Since the five segments form a complete circle, the total sum of the angles around the center is \( 360^\circ \). The angle \( \theta \) is formed by the intersection of two segments at each vertex. Therefore, we divide \( 360^\circ \) by 5 to get the value of \( \theta \). Hence, we have: \[ \theta = \frac{360^\circ}{5} = 36^\circ. \] Thus, the value of \( \theta \) is \( 36^\circ \). Final Answer: \( 36^\circ \)