In the figure, ABCD is a kite with AB = AD, BC = CD and O. If then a – b + c – d + e – f =

The correct answer is: 55

A polygon is a closed plane figure that is circumscribed by finite line segments. A quadrilateral is a 4-sided polygon.
A quadrilateral known as a kite has diagonals that connect at right angles and two pairs of adjacent sides that are equal in length.
Here we have given a figure as:

From SSS rule of congruency, we can say that:
angle b = 50 degree
From angle sum property of a triangle, we can say that:
f = 180 - (90+50) 
angle f = 40 degree
From angle sum property of a triangle, we can say that:
e = 180 - (90+50) 
angle e = 40 degree
From SSS rule of congruency, we can say that:
angle d = 25 degree
In triangle ADC, we have:
A + D + C = 180 degree
25 + 50 + c + 40 = 180
c = 180 - 115
angle c = 65 degree
From CPCT, we can say that:
angle ABC = angle ADC
a + b = c + 50
a = 65 + 50 - 50
angle a = 65 degree
a – b + c – d + e – f = 65 - 50 +65 - 25 + 40 - 40 = 55

Here we used the concept of kite and using the properties of kite and the triangles, we found the angles first. We used the congruency test to find the angles and the CPCT as well. So the value of a – b + c – d + e – f is 55.