Q:

# HELP PLEASE! FAST!! 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.

Accepted Solution

A:
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 :)