1 votes 1 votes Five line segments of equal lengths, $\text{PR, PS, QS, QT}$ and $\text{RT}$ are used to form a star as shown in the figure above. The value of $\theta$, in degrees, is _______________ $36$ $45$ $72$ $108$ Quantitative Aptitude gatecivil-2021-set1 numerical-ability geometry + – Arjun asked Feb 19, 2021 recategorized Apr 11, 2021 by Lakshman Bhaiya Arjun 13.0k points answer See all 0 reply
Best answer 2 votes 2 votes $\textbf{Central Angle Theorem:}$ The Central Angle Theorem states that the central angle from two chosen points $A$ and $B$ on the circle is always twice the inscribed angle from those two points. The inscribed angle can be defined by any point along the outer arc $AB$ and the two points $A$ and $B.$ Now, we can use the above theorem, and get the below diagram, Now, $10\theta = 360^{\circ}$ $\implies \theta = 36^{\circ}.$ So, the correct answer is $(A).$ Reference: http://jwilson.coe.uga.edu/EMAT6680Su09/Park/As8dspark/As8dspark.html Lakshman Bhaiya answered Mar 27, 2021 edited Apr 10, 2021 by Lakshman Bhaiya Lakshman Bhaiya 12.8k points comment Share See all 0 reply Please log in or register to add a comment.