Question

Quadrilateral OPQR is inscribed inside a circle as shown below. What is the measure of angle Q? You must show all work and calculations to receive credit.

Circle N is shown with an inscribed quadrilateral labeled OPQR. O is labeled 2x degrees. P is labeled y degrees. Q is labeled 2x plus 4 degrees. R is labeled 3y plus 8 degrees.

Answer 1

opposite pairs of angles of an inscribed quadrilateral add to 180°
O + Q = 180°
2x + 2x + 4 = 180°

Answer 2

okay is that all?

Answer 3

solve for x then substitute into 2x + 4 to get Q

Answer 4

i dont know how to find x

Answer 5

start by combining like terms on the left. What's 2x + 2x?

Answer 6

well i do but where do i need to find the x. i mean in which equation?

Answer 7

4x

Answer 8

2x + 2x + 4 = 180

Answer 9

^ that's the equation you need to solve for x

Answer 10

After combining you have
4x + 4 = 180
Subtract 4 from both sides

Answer 11

left withx

Answer 12

on the right side left with 174 and on the left we have x

Answer 13

not it was 176

Answer 14

sorry

Answer 15

so 4x = 176
divide by 4

Answer 16

okay 4x minus 4 is x
180 minus 4 is 176

Answer 17

it is 44

Answer 18

right. So now we can find Q.
Q = 2x + 4, so plug in 44 for x to get
Q = 2(44) + 4

Answer 19

92

Answer 20

that's the answer

Answer 21

thank you

Answer 22

you're welcome