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GATE 2021 CY – Question 8

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

Five equal-length line segments PR, PS, QS, QT and RT form the star shown. The value of θ is ______ degrees.

Diagram for GATE 2021 CY question 8
  1. 36
  2. 45
  3. 72
  4. 108

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Show answer and explanation

Correct answer: (A) 36

Explanation

For the regular star shown, the five vertices lie at 72° intervals on the circumcircle. The angle at P subtends the arc between the two lower adjacent vertices S and R. An inscribed angle is half its intercepted central angle, giving θ=72°/2=**36°, A**.