Question

Find the value of $\angle A$ + $\angle B$ + $\angle C$ +$\angle D$ + $\angle E$ from the following figure.

• A. ${300}^{\circ }$
• B. ${180}^{\circ }$
• C. ${540}^{\circ }$
• D. ${360}^{\circ }$

Answer 1

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

From the $\Delta EFG,$
$\angle E$ + $\angle F$ + $\angle G$ = ${180}^{\circ }.$
[Angle Sum Property]
$\Rightarrow$$\angle E$ + $\angle 2$ + $\angle 1$ = ${180}^{\circ }\cdot \cdot \cdot \cdot \left(i\right)$
From the $\Delta CGA$,
$\angle 1=\angle C+\angle A\cdot \cdot \cdot \cdot \left(ii\right)$
From the $\Delta FDB$,
$\angle 2=\angle D+\angle B\cdot \cdot \cdot \cdot \left(iii\right)$

Substituting $\left(ii\right)$ and $\left(iii\right)$ in $\left(i\right)$ we get
$\Rightarrow$$\angle E$ +$\angle D+\angle B$ + $\angle C+\angle A$ =${180}^{\circ }$

Rearranging terms we get,
$\angle A$ +$\angle B+\angle C$ + $\angle D+\angle E$ =${180}^{\circ }.$