1. quadrilateral abcd is inscribed in a circle.
what is the measure of angle a?

2. quadrilateral abcd is inscribed in this circle.
what is the measure of angle b?

3. quadrilateral abcd is inscribed in this circle.
what is the measure of angle a?

4. quadrilateral abcd is inscribed in this circle.
what is the measure of angle c?

1. A=  77

2. B     =140

3.  A    = 116

4. C =62

Step-by-step explanation:

For a quadrilateral inscribed in a circle, the opposite angles sum to 180

A+ C= 180

2x+9 + 3x+1 = 180

Combine like terms

5x+10 =180

Subtract 10

5x+10-10 = 180-10

5x=170

Divide by 5

5x/5 =170/5

x=34

Angle A = 2x+9

              =2(34)+9

               =68+9

               77

2.  For a quadrilateral inscribed in a circle, the opposite angles sum to 180

B+D= 180

x+4x-20 = 180

Combine like terms

5x-20 =180

Add 20 to each side

5x-20+20 =180+20

5x=200

Divide by 5

5x/5=200/5

x=40

We want angle B

B = 4x-20

    =4(40)-20

    =160-20

    =140

3.  For a quadrilateral inscribed in a circle, the opposite angles sum to 180

B+D= 180

28+x = 180

Subtract 28 from each side

28-28+x = 180-28

x =152

A = x-36

A = 152- 36

   = 116

4.   For a quadrilateral inscribed in a circle, the opposite angles sum to 180

B+D= 180

x+20 +3x = 180

4x +20 = 180

Subtract 20

4x +20-20 = 180-20

4x= 160

Divide by 4

4x/4= 160/4

x=40

Then

A + C = 180

2x+38 +C = 180

2(40) + 38 + C = 180

80 + 38 + C = 180

118 + C = 180

Subtract 118 from each side

118-118 + C = 180-118

C =62

they are simplified

step-by-step explanation:

answer: '

the distance between points l and m

step-by-step explanation: