Question

Need help with this review question. I need to know how to find the measurements from the cyclic quadrilateral

Answer 1

Given a quadrilateral ABCD

A cyclic quadrilateral has all its vertices on the circumference of the circle

Also cyclic quadrilateral

has the opposites angles add up to 180°

then

`\angle a+\angle c=180`
`\angle b+\angle d=180`

then

Option A

A=90

B=90

C=90

D=90

since A+C= 180

and B+D = 180

measures from Option A could come from a cyclic quadrilateral

Option B

A=80

B=80

C=100

D=100

Since A+C = 80+100 = 180

and B+D = 80 + 100 = 180

measures from Option B could come from a cyclic quadrilateral

Option C

A=70

B=110

C=70

D=110

Since A+C=70+70 = 140

And B+D =110+110=220

measures from Option C could NOT come from a cyclic quadrilateral

Option D

A=60

B=50

C=120

D=130

A+C= 60+120 = 180

B+D= 50+130 = 180

measures from Option D could come from a cyclic quadrilateral

Option E

A=50

B=40

C=120

D=150

A+C=50+120= 170

B+D=40+150 = 190

measures from Option E could NOT come from a cyclic quadrilateral

Then correct options are

Options

A,B and D