Question

Find the value of X and each arc measure.

Answer 1

@Az

Answer 2

What would you say about the arcs MN and QP?

They're formed by vertical angles

so are they equal to each other or do they add up to 180?

Answer 3

equal to each other, i would say

Answer 4

Exactly! So set it equal to each other and solve

10x - 45 = 6x - 1

Answer 5

x = 11

Answer 6

how would i find NP

Answer 7

So first let's find the other ones and then we can find NP

MN is 10x - 45

plug in x = 11 and what do you get?

Answer 8

65 for both

Answer 9

Good and you know that those two other angles are going to all add to 360

65 + 65 + NP + NP = 360

so what is NP?

Answer 10

25?

Answer 11

No no

think of NP as 'a'

65 + 65 + a + a = 360

can you solve for 'a'

Answer 12

NP is just the angle of that arc and all those angles make a whole circle so it adds up to 360

Answer 13

I know that 65+65 =130

Answer 14

yes and if you have one apple + one apple

then that's two apples

130 + 2a = 360

it's just like how you solve for 'x'

'a' is just basically another letter just like 'x'

Answer 15

Im kinda confused, like i understand the concept

Answer 16

okay so basically this is what we have right now



all those four angles add up to 360

so basically we're trying to solve for that angle 'x' or 'a' so that way we can find the arc NP

Answer 17

idk tbh

Answer 18

im struggling with this

Answer 19

how were you solving for x before?

65 + 65 + x + x = 360

130 + 2x = 360

we want to get x all by itself

so first subtract 130 on both sides

130 - 130 + 2x = 360 - 130

2x = 360 - 130

what is 360 - 130 = ??

Answer 20

230

Answer 21

good so

2x = 230

and we want x all by itself so we divide 2 on both sides

2x/2 = 230/2

x = ??

what is 230/2

Answer 22

115

Answer 23

so that's what the angle of NP is so what is arc NP??

Answer 24

NP is 115

Answer 25

Exactly!!

And now what about NQP

Answer 26

245

Answer 27

And that's your answer!

Answer 28

thank you

Answer 29

No problem!