Question

What is the sum of angles that are marked in the given figure?

• A. ${360}^{\circ }$
• B. ${540}^{\circ }$
• C. ${720}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

The correct option is A ${360}^{\circ }$


In $△ABP$, $\angle P$ = ${180}^{\circ }$ - ($\angle A$ + $\angle B$ )
In $△CDQ$, $\angle Q$ = ${180}^{\circ }$ - ($\angle C$ + $\angle D$ )
In $△EFR$, $\angle R$ = ${180}^{\circ }$ - ($\angle E$ + $\angle F$ )
In $△HGS$, $\angle S$ = ${180}^{\circ }$ - ($\angle H$ + $\angle G$ )

In the quadrilateral PQRS,
($\angle P$ + $\angle Q$ + $\angle R$ + $\angle S$ ) = ${360}^{\circ }$
$\Rightarrow$ ${180}^{\circ }$ - ($\angle A$+ $\angle B$ )
+ ${180}^{\circ }$ - ($\angle C$ + $\angle D$ )
+ ${180}^{\circ }$ - ($\angle E$ + $\angle F$ )
+ ${180}^{\circ }$ - ($\angle H$ + $\angle G$ ) = ${360}^{\circ }$

$\Rightarrow$ ${720}^{\circ }$ - ($\angle A$ + $\angle B$) - ($\angle C$ + $\angle D$)
- ($\angle E$ + $\angle F$ ) - ($\angle H$ + $\angle G$ ) = ${360}^{\circ }$

$\Rightarrow$ $\angle A$ + $\angle B$ + $\angle C$ + $\angle D$ + $\angle E$ + $\angle F$ + $\angle H$ + $\angle G$ = ${360}^{\circ }$