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​1. Quadrilateral ABCD ​ is inscribed in this circle.
What is the measure of angle B?


2. ​ Quadrilateral ABCD ​ is inscribed in this circle.
What is the measure of angle A?


3. ​ Quadrilateral ABCD ​ is inscribed in this circle.
What is the measure of angle C?

1 Quadrilateral ABCD is inscribed in this circle What is the measure of angle B 2 Quadrilateral ABCD is inscribed in this circle What is the measure of angle A class=
1 Quadrilateral ABCD is inscribed in this circle What is the measure of angle B 2 Quadrilateral ABCD is inscribed in this circle What is the measure of angle A class=
1 Quadrilateral ABCD is inscribed in this circle What is the measure of angle B 2 Quadrilateral ABCD is inscribed in this circle What is the measure of angle A class=

Respuesta :

1) The opposite angles of a inscribed quadrilateral are supplementary.

3x - 12 + x = 180
4x - 12 = 180 
4x = 192
x = 48

Now we know the value of x we can substitute it for x in the expression of angle B.

3(48) - 12 = 132

Angle B is 132°

2) The opposite angle of an inscribed quadrilateral are supplementary. So first we will find the value of x.

28 + x = 180
x = 152

The value of x is 152 so we can substitute this in for x in the expression of angle A.

152 - 36 = 116

So angle A is 116°

3) To find the measure of angle C we will first find the value of x.

3x + 9 + 2x - 4 = 180
5x + 5 = 180
5x = 175
x = 35

Now we can find the value of angle A an then subtract it by 180 for angle C.

2(35) + 3 = 73

180 - 73 = Angle C 
107 = Angle C

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