Question

Find four angles of a cyclic quadrilateral ABCD in which angle A=(2x-1), angle B=(y+5), angle C=(2y+15), angle D=(4x-7) and angle A+angle C=180°

Answer 1

Answer:

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Answer 2

Answer:

∠A=65, ∠B=55, ∠C=115, ∠d=125

Step-by-step explanation:

we know that the sum of opposite angles of a cyclic quadrilateral is 180°

∠A+∠C=180

(2x-1)+(2y+15)=180

2x+2y+14=180

2x+2y=180-14

2x+2y=166

dividing equation by 2

x+y=83   (1)

and

∠B+∠D=180

(y+5)+(4x-7)=180

y+5+4x-7=180

4x+y-2=180

4x+y=182    (2)

on subtracting (1)  from (2), we get

3x=182-83

3x=99

x=99/3

x=33

putting x=33 in (1)

33+y=83

y=83-33

y=50

thus x=33, y=50

∠A=2x-1

=2×33-1

=66-1

=65

∠B=y+5

=50+5

=55

∠C=2y+15

=2×50+15

=100+15

=115

∠D=4x-7

=4×33-7

=132-7

=125