Question

Five line segments of equal lengths PR, PS, QS, QT and RT as used to form a star shown in the figure below.


The value of $\theta$, in degress, is _____.

• A.
  72
• B.
  108
• C.
  36
• D.
  45

Answer 1

The correct option is C

36

$\text{Sum of angle formed at the pentagon}={540}^{\circ }$

$\text{Each angle of pentagon}=\frac{540}{5}={108}^{\circ }$
$\angle x=180-108={72}^{\circ }$

$Sumofangleoftriangle={180}^{\circ }$

${72}^{\circ }+{72}^{\circ }+\theta ={180}^{\circ }$

$\theta ={36}^{\circ }$