Question

Quadrilateral OPQR is inscribed in circle N. What is the measure of RQP?

Answer 1

180 = (2x +19) + (6x - 5)
180 = 2x + 19 + 6x - 5
8x + 14

I'm stuck here.

Answer 2

Do I subtract 14 from 180?

Answer 3

166/8 = 8x/8
Then I'm getting x = 20.75?

Answer 4

lol

Answer 5

okay?

Answer 6

hold brb

Answer 7

sure

Answer 8

back

Answer 9

is what I'm doing correct? I'm confused

Answer 10

$2x+19+\left(6x-5\right)=180$2x+19+(6x−5)=180


$\mathrm{Refine}$Refine

$8x+14=180$8x+14=180



$\mathrm{Subtract\:}14\mathrm{\:from\:both\:sides}$Subtract 14 from both sides

$8x+14-14=180-14$8x+14−14=180−14


$8x=166$8x=166



$\mathrm{Divide\:both\:sides\:by\:}8$Divide both sides by 8

$\frac{8x}{8}=\frac{166}{8}$8x8 =1668

$x=\frac{83}{4}$x=8/34

Answer 11

I'm still confused. How is x = 8/34? I have to substitute x into the next formula.

Answer 12

2x+19+(6x−5)=180

Answer 13

8x+14=180

Answer 14

8x=166

Answer 15

x=834

Answer 16

83/4

Answer 17

So then it would be (2(83/4) +19) + (6x - 5)?

Answer 18

yep

Answer 19

i think

Answer 20

Hey @usercode3rror

Answer 21

hey @error1603

Answer 22

hey @Eroor1603

Answer 23

@Error1603 hey bro

Answer 24

but wouldn't simplifying 166/8 = 20.75? I don't know this is my first time working this out so you are probably correct.

Answer 25

166/8 reduces

Answer 26

Then it would be (41.5 + 19) + (6x - 5)?

Answer 27

Oh okay

Answer 28

Okay, so opposite angles in inscribed quadrilaterals are supplementary (adding up to 180 degrees). So...set up an equation using angles ROP and RQP. Solve for x: (x + 17) + (6x - 5) = 180 Then...plug the value of x into the equation for angle QRO, which is (2x + 19), and solve.

Answer 29

Okay

Answer 30

But I already set it up. This is what I have so far.
180 = (2x + 19) + (6x - 5)
180 = 2x + 19 + 6x - 5
8x + 14
166 = 8x
x = 83/4
(2(83/4) + 19) + (6x - 5)
(41.5 + 19) + (6x - 5)

Answer 31

I just need someone to tell me if I'm doing this correctly

Answer 32

all u need to do is solve now

Answer 33

x + 17) + (6x - 5) = 180
7x+12 = 180
7x = 168
x = 24
(2x + 19)
2(24) + 19
48 + 19 This is my way

Answer 34

$\left(41.5+19\right)+\left(6x-5\right)=6x+55.5$(41.5+19)+(6x−5)=6x+55.5

Answer 35

6x+55.5​

Answer 36

But that's not correct @Error1603 That's for angle OPQ.

Answer 37

I'm trying to solve for RQP

Answer 38

=6x+55.5​

Answer 39

oooooh okay

Answer 40

Does RQP = 119.5?

Answer 41

yea @Error1603 lol

Answer 42

I got 67

Answer 43

@Error1603 How did you get 67?

Answer 44

=\frac{12x+111}{2}

Answer 45

here katniss

Answer 46

$\left(2\left(\frac{83}{4}\right)+19\right)+\left(6x-5\right)=\frac{12x+111}{2}$(2(834 )+19)+(6x−5)=12x+1112
Steps

$\left(2\left(\frac{83}{4}\right)+19\right)+\left(6x-5\right)$(2(834 )+19)+(6x−5)

$\mathrm{Remove\:parentheses}:\quad\left(a\right)=a$Remove parentheses: (a)=a

$=2\cdot\frac{83}{4}+19+6x-5$=2·834 +19+6x−5


Show Steps
$\mathrm{Join}\:2\cdot\frac{83}{4}:\quad\frac{166}{4}$Join 2·834 : 1664
$=\frac{166}{4}+19+6x-5$=1664 +19+6x−5



Show Steps
$\frac{166}{4}:\quad\frac{83}{2}$1664 : 832
$=\frac{83}{2}+19+6x-5$=832 +19+6x−5


$\mathrm{Add/Subtract\:the\:numbers:}\:19-5=14$Add/Subtract the numbers: 19−5=14

$=6x+14+\frac{83}{2}$=6x+14+832


$\mathrm{Convert\:element\:to\:fraction}:\quad\:6x=\frac{6x}{1},\:14=\frac{14}{1}$Convert element to fraction: 6x=6x1 , 14=141
$=\frac{6x}{1}+\frac{14}{1}+\frac{83}{2}$=6x1 +141 +832


Show Steps
$\mathrm{Find\:the\:LCD\:for}\:\frac{6x}{1}+\frac{14}{1}+\frac{83}{2}:\quad2$Find the LCD for 6x1 +141 +832 : 2


$\mathrm{Adjust\:Fractions\:based\:on\:the\:LCD}$Adjust Fractions based on the LCD

$=\frac{6x\cdot\:2}{2}+\frac{14\cdot\:2}{2}+\frac{83}{2}$=6x· 22 +14· 22 +832


$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad\frac{a}{c}\pm\frac{b}{c}=\frac{a\pm\:b}{c}$Since the denominators are equal, combine the fractions: ac ±bc =a± bc
$=\frac{2\cdot\:6x+2\cdot\:14+83}{2}$=2· 6x+2· 14+832


Hide Steps
$\mathrm{Simplify}\:2\cdot\:6x+2\cdot\:14+83:\quad12x+111$Simplify 2· 6x+2· 14+83: 12x+111


$2\cdot\:6x+2\cdot\:14+83$2· 6x+2· 14+83


$\mathrm{Multiply\:the\:numbers:}\:2\cdot\:6=12$Multiply the numbers: 2· 6=12

$=12x+2\cdot\:14+83$=12x+2· 14+83



$\mathrm{Multiply\:the\:numbers:}\:2\cdot\:14=28$Multiply the numbers: 2· 14=28

$=12x+28+83$=12x+28+83



$\mathrm{Add\:the\:numbers:}\:28+83=111$Add the numbers: 28+83=111

$=12x+111$=12x+111



$=\frac{12x+111}{2}$=12x+1112 ​

Answer 47

Sorry that for OPQR

Answer 48

180 = (2(83/4) + 19)
180 = (41.5 + 19)
180 = 60.5
RQP = 119.5

Answer 49

@usercode3rror I only see letters

Answer 50

I'm messing up

Answer 51

@Error1603 it's okay

Answer 52

ima solve it foe u

Answer 53

But I just solved it omg

Answer 54

I just need you to tell me if it's right

Answer 55

i got that

Answer 56

So I wouldn't round to 119?

Answer 57

no round to 120

Answer 58

Okay

Answer 59

this was fun