Question

ss below

Answer 1

@AZ

Answer 2

?

Answer 3

okay, so this one is going to be a little bit more work but just bear with me

Do you remember the formula from the previous problems?

angle = 1/2 * (big arc - small arc)

Answer 4

yes

Answer 5

so what is the big arc in the image and what is the small arc?

use the letters on the circle

Answer 6

the big arc is wz and the small one is xy

Answer 7

@AZ

Answer 8

@florisalreadytaken

Answer 9

Good! And the angle is P

so far we have

P = 1/2 (WZ - XY)

Do you agree?

Answer 10

Now

WZY = 200

WZY is basically WZ + ZY and that equals 200

Now if that equals 200, what does the rest of the circle equal?

The entire circle adds up to 360

so what is 360 - 200 = ?

Answer 11

im sorry i didnt respond something happened to my brother

Answer 12

@AZ its my last question

Answer 13

okay, I hope your brother is fine

read my last comments and respond to it

Answer 14

its 160

Answer 15

and yeah he will be ok

Answer 16

its ok thanks for looking at it

Answer 17

no problem :D

Answer 18

so the rest of the circle is 160

that means WXY is 160

do you agree?

Answer 19

yes

Answer 20

and WXY is WX + XY

right?

Answer 21

yes?

Answer 22

so now let's put everything together

you said the big arc was WZ and the small arc was XY

and so the formula for the angle was

P = 1/2 (WZ - XY)

and now we know

WZY is equal to WZ + ZY = 200

and WXY is equal to WX + XY = 160

Do you follow still?

Answer 23

kinda but yes

Answer 24

okay, do you see in the image how there's that red dash on the both lines?

Answer 25

that just means that those two line segments have the same length

which means that the arcs opposite that are the same

so basically WX = ZY

Answer 26

ok

Answer 27

okay so you know how we have

P = 1/2 (WZ - XY)

we want to substitute those two other equations into this one so we can solve for P

Answer 28

WZ + ZY = 200

can you solve for WZ

Answer 29

yes

Answer 30

it would be half right

Answer 31

no, it would just be WZ = 200 - ZY

Answer 32

can you do it similarly for

WX + XY = 160

solve for XY

just subtract WX on both sides

Answer 33

ya lost me

Answer 34

again :(

Answer 35

so basically, think of it like apples and oranges

WX is an apple
XY is an orange

WX + XY = 160

apple + orange = 160

now what is an orange?

orange = 160 - apple

does that make sense?

Answer 36

so i have to divide 160?

Answer 37

no

Answer 38

you only divide if you were multiplying before to move it to the other side

now we need to substitute it in

Answer 39

ok

Answer 40

P = 1/2 (WZ - XY)

WZ = 200 - ZY
XY = 160 - WX

and remember how we said ZY = WX
so instead having both, we can just one for consistency

WZ = 200 - ZY
XY = 160 - ZY

Answer 41

let me add colors

\( P = \dfrac{1}{2} (\color{red}{WZ} - \color{lime}{XY})\)

\(\color{red}{WZ} = 200 - ZY\)
\(\color{lime}{XY} = 160 - ZY\)

Answer 42

ok what about them now

Answer 43

you plug it in

\( P = \dfrac{1}{2} (\color{red}{200 - ZY} - (\color{lime}{160 - ZY}))\)

Answer 44

ok so 200-160 then divide by 2

Answer 45

exactly

Answer 46

ohh ok ill do that

Answer 47

i got 920.5?

Answer 48

oops i pressed plus sorry

Answer 49

its 20

Answer 50

There you go

Answer 51

This question was so long and extra

Answer 52

yeah it was

Answer 53

but thx

Answer 54

you're welcome