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?

if you do not know, do not answer just for points. you will be reported.

1) Opposite angles of an inscribed quadrilateral are supplementary.

x + 4x - 20 = 180
5x - 20 = 180
5x = 200
x = 40

2) We will use angle B and D to find the value of x first.

148 + x = 180
x = 32

now we will substitute this x in the value of angle A.

2x + 1 = A
2(32) + 1 = A
65 = A

3) First we will find the value of x. For that we will use the angles B and D.

x + 10 + x + 24 = 180
2x + 34 = 180
2x = 146
x = 73

So the value of x is 73. We can use that to find angle A.

x + 15 = A
73 + 15 = A
88 = A

Now we can find angle C because A and C are supplementary due to the inscribed angle theorem.

180 - 88 = C
 92 = C

Hope it helps :)

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