Question

In the figure, if $\angle A+\angle B+\angle C+\angle D+\angle E+\angle F=$ k right angles, then k is

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (C)

4

In $△ABC$ using angle sum property of triangle

$\angle A+\angle B+\angle C={180}^{\circ }......\left(i\right)$

Similarly in $△DEF$

$\angle D+\angle E+\angle F={180}^{\circ }......\left(ii\right)$

Adding $\left(i\right)$ and $\left(ii\right)$

$\Rightarrow \angle A+\angle B+\angle C+\angle D+\angle E+\angle F={180}^{\circ }+{180}^{\circ }$

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

$k\left({90}^{\circ }\right)={360}^{\circ }$

$\Rightarrow k=\frac{{360}^{\circ }}{{90}^{\circ }}=4$