Maths-
General
Easy

Question

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

Hint:

## 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 degreeFrom angle sum property of a triangle, we can say that:f = 180 - (90+50) angle f = 40 degreeFrom angle sum property of a triangle, we can say that:e = 180 - (90+50) angle e = 40 degreeFrom SSS rule of congruency, we can say that:angle d = 25 degreeIn triangle ADC, we have:A + D + C = 180 degree25 + 50 + c + 40 = 180c = 180 - 115angle c = 65 degreeFrom CPCT, we can say that:angle ABC = angle ADCa + b = c + 50a = 65 + 50 - 50angle a = 65 degreea – 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.