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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 _______________

  1. $36$
  2. $45$
  3. $72$
  4. $108$
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$\textbf{Central Angle Theorem:}$  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

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