Discussion
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 θ, in degrees, is ______
Answer: A
The angle θ is 36 degrees.
Five equal segments joined this way form a regular pentagram, whose vertices lie on a regular pentagon. The angle at a point of the star is an inscribed angle standing on one side of that pentagon, which subtends 360/5 = 72 degrees at the centre:
\[ \theta = \frac{1}{2} \times 72^{\circ} = 36^{\circ} \]
Check: the five point angles of any five-pointed star add up to 180 degrees, and 5 × 36 = 180. 72 degrees is the central angle, 108 degrees is the interior angle of the pentagon, and 45 has no place in a five-fold figure.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development