Question

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?

Answer 1

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➷ 1) Opposite angles in a cyclic quadrilateral equal 180 degrees

2x + 9 + 3x + 1 = 180

Simplify:

5x + 10 = 180

Subtract 10:

5x = 170

Divide by 5:

x = 34

2(34) + 9 = 77

angle A = 77 degrees.

2) Again, use the same rule.

4x - 20 + x = 180

Simplify:

5x - 20 = 180

Add 20:

5x = 200

Divide by 5:

x = 40

4(40) - 20 = 140

Angle B = 140 degrees.

3) Again, use the same rule but in a slightly different way.

180 - 28 = 152.

Subtract 28

x = 152

152 - 36 = 116.

Angle A = 116 degrees.

4) Use the same rule.

3x + x + 20 = 180

Simplify

4x + 20 = 180

Subtract 20

4x = 160

Divide by 4:

x = 40

2(40) + 38 = 118

180 - 118 = 62

Angle C = 62 degrees.

➶Hope This Helps You!

➶Good Luck :)

➶Have A Great Day ^-^

↬ Hannah ♡

Answer 2

1. A= 77

2. B =140

3. A = 116

4. C =62

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