question_answer

ABCDE is a regular pentagon. Alternate vertices are joined to make a fivepointed star ACEBDA. The sum of the 5 vertical angles of this star is

A)  1 rt. angle          

B)  2 rt angle  

C) \[270{}^\circ \]

D) \[300{}^\circ \]

Correct Answer: B

Solution :

 Vertical Angle of the five pointed star ACEBDA \[=\frac{1}{3}\times \frac{(2\times 5-4)\times {{90}^{o}}}{5}={{36}^{o}}\] \[\therefore \] Sum of the 5 vertical angles of this star                 \[=5\times {{36}^{o}}\]                 \[={{180}^{o}}=2\,rt.\] angles