Five line segments of equal lengths, PR, PS, QB, 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

GATE 2021 · General Aptitude · Geometry · medium

Answer: theta = 36 degrees

1. Interior angle of the regular pentagon: For n = 5: interior angle = (5-2)*180/5 = 3*180/5 = 540/5 = 108 degrees
2. Base angles of each tip triangle: At each base vertex of a tip triangle, the angle inside the triangle = 180 - 108 = 72 degrees
3. Compute the tip angle theta: theta = 180 - 72 - 72 = 180 - 144 = 36 degrees