Question

Abcd is a cyclic quadrilateral such that angle a =4y+20°,b =3y-5°,c=4x°,d=7x+5° .Find the four angles

Answer 1

Concept:

Opposite angles of a cyclic quadrilateral

are supplementary.

Given:

∠A = 4y+20

∠B = 3y-5

∠C = - 4x

∠D = 7x+5

since Opposite angles of a cyclic quadrilateral are supplementary,

we have

∠A+∠C = 180°

4y+20-4x = 180

-4x+4y = 160

-x+y = 40.........(1)

and

∠B+∠D = 180°

3y-5+7x+5 = 180

7x+3y= 180.....(2)

-7x+7y= 280 (multiplying (1) by 7)

10y = 460

y= 46

(1)gives

-x+46=40

-x= -6

x=6

Answer 2

Answer:

in a cyclic quadrilateral sum of oposite angle =180

ang. a is opposite to ang. c

similarly ang. b to ang. d

4y +20 + 4x = 180

3y - 5 +7x+ 5 = 180

now just solve these two with elimination or subditution and you will get your x and y

hope it helps

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