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 =

- 50
- 55
- 60
- 65

Hint:

### A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees. Here we have to find the value of 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.

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