Question

In figure $ABCDE$, find $\angle 1+\angle 2+\angle 3+\angle 4+\angle 5$.

Answer 1

In $△ABE,$

$\Rightarrow$ $\angle A+\angle ABE+\angle AEB={180}^o$ ---- ( 1 )

In $△BDE,$

$\Rightarrow$ $\angle DBE+\angle BDE+\angle BED={180}^o$ ----- ( 2 )

In $△BCD,$

$\Rightarrow$ $\angle CBD+\angle C+\angle CDB={180}^o$ ---- ( 3 )

Adding equation ( 1 ), ( 2 ) and ( 3 )

$\Rightarrow$ $\angle A+\angle ABE+\angle AEB+\angle DBE+\angle BDE+\angle BED+\angle CBD+\angle C+\angle CDB={180}^o+{180}^o+{180}^o$

$\Rightarrow$ $\angle A+\angle B+\angle C+\angle D+\angle E={540}^o$