Question

Would appreciate help with this problem. Ss below :)

Answer 1

I got that NK = 12 and JK = 24 but i don't know the other two?

Answer 2

What would be mNLK?

Answer 3

For arcs MK and JPK, we can start by calculating the circumference of the entire circle.
We know the radius of the circle from LK, 15. From that, we know that the circumference of the circle is 2*pi*15, or 30*pi.
Now, arc MK is a fraction of the total circumference, but what fraction is that? If we find the measure of angle L in the right triangle NLK (let's call that angle L), then the length of arc MK will be (L/360)*(30*pi).
This is because the total "angle" measure of a circle is 360, so that smaller angle would be a fraction of the total 360

Answer 4

You have all three side measures of triangle NLK

Answer 5

So how would we find angle L?

Answer 6

First, to find the measure of angle L.
Based on the right triangle inside the circle, we could say that cos(L) = 9/15
From this, we can also calculate that
\[L = \cos^{-1} (9/15)\]

Answer 7

My calculations say that L would be about 53 degrees, based on the above

Answer 8

That's 53.13, so would we use the formula \ ?

Answer 9

s = r x theta*

Answer 10

I'm sorry, I'm not familiar with that formula. What do you use it for?

Answer 11

Arc length

Answer 12

No, you just need angle measures

Answer 13

I think mhanifa is right, actually, and that was my misunderstanding.
The question asks for the angle measures of the arcs, not the lengths of the arcs. Looking more closely at the question, I see that the boxes for mJPK and mMK are meant to be in degrees, so we've already found mMK, like you said

Answer 14

You found one for mMK

Answer 15

take a D and out the middle dot on each corner and then count the number you will get your answer

Answer 16

Point K is 36.9 degrees what do we do with that?

Answer 17

Please ignore point K

Answer 18

oh ok

Answer 19

This is fortunate for us, since we don't have to do quite as much work.
mJM happens to be symmetrical with mMK, across line ML; the angle measures are the same.
So, (though the question does not ask for it) we know mJM is 53.13, just as mMK is 53.13. That gives us a total of 106.26 degrees in those two arcs. And it just so happens that arc JPK spans the entire rest of the circle.
So, to find mJPK, we just have to calculate 360 - 106.26. Unless I am mistaken, of course

Answer 20

SmokeyBrown you are correct

Answer 21

Yay we got it all right :D Thanks guys

Answer 22

The perpendicular bisector of JK, that passes through the center makes JN = NK and respective arcs mJM = mJK

Answer 23

Congrats