Question

In the figure, the value of $ \angle A+\angle B+\angle C+\angle D+\angle E+\angle F$ is:

• A. $190°$
• B. $540°$
• C. $360°$
• D. $180°$

Answer 1

The correct option is C

$360°$

Step 1: Calculate the sum of group of three angles

In the given figure, it can be clearly observed that the diagram consists of two triangles $△ABC$ and $△DEF$.

Now, using the angle sum property in $△ABC$, we get,

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

Again, using the angle sum property in $△DEF$, we get,

$\angle D+\angle E+\angle F=180°$ $...\left(\mathrm{i}\right)$

Step 2: Calculate the required sum

Now, on adding the equation $\left(\mathrm{i}\right)$ and $\left(\mathrm{ii}\right)$, we get,

$\angle A+\angle B+\angle C+\angle D+\angle E+\angle F=180°+180°$

$\Rightarrow \angle A+\angle B+\angle C+\angle D+\angle E+\angle F=360°$

Hence, option (C) is the correct option.