Question

Find the value of X and each arc measures.

Answer 1

@snowflake0531

Answer 2

Look at the circle

remember that the total angles add up to 360 in a circle

and half of a circle would be 180 degrees

so do you see how EF and FG would add up to 180?

Answer 3

yes

Answer 4

so add them up and set it equal to 180

and solve for x

Answer 5

so like 12x-23=x-3?

Answer 6

no, you just set them equal to each other

is EF equal to FG??

no, they add up to equal 180

Answer 7

i'm a little confused

Answer 8

That's half a circle and it's equal to 180

Answer 9

EF is x-3

FG is 12x - 25

if you ADD them together, then it should EQUAL 180

Answer 10

x would be 16?

Answer 11

how would i find DE

Answer 12

12x - 25 + x - 3 = 180

13x - 28 = 180
13x = 208

x = 16

so yes, you got the value of x correct!

Answer 13

To find DE, you just plug in that value

We know that DE is opposite FG so that means they're both equal

and FG is 12x - 25

so replace x with 16 and solve

12(16) - 25 = ??

Answer 14

167?

Answer 15

That's correct!!

Now what about EF

EF is x - 3

so replace x with 16

Answer 16

13

Answer 17

There you go and now

DFG

Answer 18

347?

Answer 19

That's correct

did that make sense?

Answer 20

Yes so DE = 167 EF = 13 ans DFG = 347

Answer 21

yes and x = 16

Answer 22

thank you

Answer 23

no problem!