Question

find the sum of the angle abc + angle cde in the figure given

Answer 1

answer is 540...because it is pentagon

Answer 2

to be 540 degrees both the angles have to be more than 180 degrees ... the actual answer is 270 degrees

Answer 3

It is half of an octagon. Four sides in the top half is shown and four sides in the bottom half not shown.

The external degrees of a polygon always adds up to 360 degrees.

So the external angle for an octagon is 360/8 = 45 degrees.

The internal angle must be 180 - 45 = 135 degrees.

ABC = 135 ; CDE = 135 So their sum is 270 degrees.

Answer 4

@Ranga : no where in the problem it is said that sides AB, BC, CE etc are equal, so why sould we assume it to be a regular polygon (octagon in this case )

Answer 5

In the drawing it looked like the sides AB, BC, CE etc were equal. Even if they are not the answer is still 270 degrees.

Answer 6

ABC + CDE = b1 + b2 + d1 + d2 = ?

a1 + b1 + b2 + c1 + c2 + d1 + d2 + e = 540 degrees (sum of interior angles of an irregular five-sided polygon). ----- (1)

Another way to derive it is: there are 4 triangles and so the sum of all the angles add up to 180 x 4 = 720. Subtract the 180 degrees formed by AE that includes all angles at the center and you are left with 540 degrees for the sum of interior angles..
Now because they are isosceles triangles due to the same radius of circle
a1 = b1; c1 = b2; c2 = d1; e = d2. Replace in equation (1)
b1 + b1 + b2 + b2 + d1 + d1 + d2 + d2 = 540
2(b1 + b2 + d1 + d2) = 540
(b1 + b2 + d1 + d2) = 270
ABC + CDE = 270

Answer 7

@ranga : Thanks a lot !! I think the last way is the best way !!

Answer 8

you are welcome!