The angles of cyclic quadrilateral ABCD are angle A=(6x+30) B= 5x, C= x+10 D=3y-10
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As per the rule
=>Sum of Opposite angle of a cyclic quadrilateral is 180°
So, following this rule
angle A+angleC=180°
(6x+30)+(x+10)=180
6x+30+x+10=180
7x+40=180
7x=180-40
7x=140
x=20
angle B+angle D=180
5x+3y-10=180
5×20+3y-10=180
100+3y-10=180
90+3y=180
3y=180-90
3y=90
y=30
angle A=6x+30
=6×20+30
=120+30
=150
angle B=5x
=5×20
=100
angle C=x+10
=20+10
=30
angle D=3y-10
=3×30-10
=90-10
=80
@Altaf
=>Sum of Opposite angle of a cyclic quadrilateral is 180°
So, following this rule
angle A+angleC=180°
(6x+30)+(x+10)=180
6x+30+x+10=180
7x+40=180
7x=180-40
7x=140
x=20
angle B+angle D=180
5x+3y-10=180
5×20+3y-10=180
100+3y-10=180
90+3y=180
3y=180-90
3y=90
y=30
angle A=6x+30
=6×20+30
=120+30
=150
angle B=5x
=5×20
=100
angle C=x+10
=20+10
=30
angle D=3y-10
=3×30-10
=90-10
=80
@Altaf
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