Question

In the above figure, what is the value of
$\angle$1 + $\angle$2 + $\angle$3 + $\angle$4 ?

• A. 210${}^{\circ }$
  
• B. 180${}^{\circ }$
  
• C. 150${}^{\circ }$
• D. 120${}^{\circ }$
  

Answer 1

The correct option is B 180${}^{\circ }$


Using Legendre's Theorem we find,

in $△$ABD,
$\angle$1 + $\angle$3 + 90${}^{\circ }$ = 180${}^{\circ }$.
$\therefore$ $\angle$1 + $\angle$3 = 90${}^{\circ }$............(i)
Similarly, in $△$BCD,
$\angle$2 + $\angle$4 + 90${}^{\circ }$ = 180${}^{\circ }$.
$\therefore$ $\angle$2 + $\angle$4 = 90${}^{\circ }$............(ii)
Adding (i) and (ii), we get
$\angle$1 + $\angle$2 + $\angle$3 + $\angle$4 = 180${}^{\circ }$