The GATE Grind

GATE 2021 CE (CE1) – Question 8

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Five equal-length segments PR, PS, QS, QT and RT form the five-pointed star shown. Find the marked tip angle θ in degrees.

see the reproduced source diagram and its labels.
  1. 36
  2. 45
  3. 72
  4. 108

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 36

Explanation

The equal chords define the regular five-pointed star. Its five outer vertices divide the circumcircle into 72° arcs. The angle at P subtends the adjacent arc RS, so the inscribed-angle theorem gives $\theta=72^\circ/2=\mathbf{36^\circ}$, **A**.