9th Class
Mathematics
Geometry
Question Bank
Geometry
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