Question

In the given figure, find the $\mathrm{\angle }$($A+B+C+D+E+F+G$)=

Answer 1

Hint: If you observe the given figure it has 7 vertices. This figure is Heptagon. Heptagon is a polygon with 7 sides. To find all the required sum of angles, we apply the formula of the interior angles.

Complete step by step answer:
Sum of interior angles of an n sides polygon =$\left(2n-4\right)\times 90$degrees…… $\left(1\right)$
Let us find the sum of interior angles of a heptagon.
So, the total number of sides in heptagon=7
Then n=7
From equation $\left(1\right)$,we have
Sum of interior angle of a heptagon=$\left(2\times 7-4\right)\times 90$
$\Rightarrow 10\times 90=900$
One angle of a heptagon =${\displaystyle \frac{900}{7}}=128.57$degree
So, one angle of a triangle=$180-128.57$
$=51.43$ degrees
Another angle is $180-102.85$
$=77.14$degrees

Therefore, the sum of $\mathrm{\angle }$(A+B+C+D+E+F+G)=$77.17\times 7=540$degrees

Note:
Remember the formula of the sum of the interior angle of the “n” sides polygon. And the sum of all the angles of a triangle is 180 degrees. We need to be careful while observing the given figure to decide n value.