Question

Guys pls help me to solve this problem.I need a clear explanation guys

Answer 1

hey!!

here is your answer >>>

angle DBC = In the middle of the star , we can find an angle named X, If we find that angle, we can find the angle DEF!. That angle x is inscribed inside a pentagon!. This pentagon has all the sides equal, according to the question!. Now let us find the angle x.

The total angle of a pentagon is 540° ..

how? > The formula to find the total angle is

(n - 2) 180!.

n is the number of sides!.

Pentagon has 5 sides!. .

(5-2)180

3(180)

=> 540° ..

As all sides are equal, each angle too would be equal.

To find x , we will have to divide 540 by 5!.

540/5


=> 108°!.

Then angle DBC would be 180-108

=> 72°!. (straight angle).

Now, angle DEF

As we know, each angle of a pentagon is 108°.

BDF and HFD would also be 108°>>>

Then, DFE and FDE would be 72° (straight angle ). Angle DEF would be

180-(72+72)

180- 144

36°!.

As the total sum of angles in a triangle is 180°!.



I guess the geometric name of a start is star polygon!.

Hope my answer helps!