Question

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

• A. 1 rt. angle
• B. 2 rt. angle
• C. 270${}^o$
• D. 300${}^o$

Answer 1

The correct option is B 2 rt. angle

Vertical Angle ofthe 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 $=5\times {36}^o={180}^o=2rt.$ angles