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GATE 2021 IN – Question 8

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

Five equal-length segments PR, PS, QS, QT, RT form the star shown. The angle $\theta$ is ______ degrees.

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

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Show answer and explanation

Correct answer: (A) 36

Explanation

Using the regular five-point star geometry intended by the diagram, the five vertices are equally spaced on a circle. A tip subtends one fifth of the circumference, an arc of 72°, so its inscribed angle is half of this: **36°, A**.