I'm not sure which formula to use for these. I think the other half of the circle (with 27) is 153 for that arc. The other arc near 119 is 61
If I am right how do I get x now??
I got x=30.6 but I'm probably completely wrong because I set it up like 119=5x-7+27
Where do the 119degrees 27 degrees and (23x-3) degrees belong?
The diagrams are really poor.
In the first one it looks a like (5x-7) and 27degrees are vertically opposite. In which case they are equal.
BUT then where does the 119 degrees belong ..... or ..... is 119 a length.... 119 inches perhaps?
Can you tell us what the diagram says please, I mean what are the tiny symbols ?
They are each degrees. 119 degrees is just one of the arcs and 5x-7 is another degree in between 119 and 27 (so the angle I'm guessing). 27 degrees is the other arc given. It doesn't really say much this is all it provides. I'm not gonna worry about the second one yet since it literally gives me no information.
If they are all degrees the first one makes no sense whatsoever.
The second one really does not indicate which is the algebraic angle.
I think that they are both rubbish questions.
Wow...I'm glad someone agrees with me. My teacher didn't give me anything to go off of either! I'm thinking of asking her how exactly she wants me to solve these problems but whenever I ask for help she never actually helps me.
Oh also the formula given (which is clearly not right with this problem unless I need to find the other arcs first) is a*b=c*d. I'm including a picture so you know what i'm talking about:
This is interesting but if the first ones are all angles I cannot see how this relates.
Ae these sheets the teacher has given you or out of a text book or what?
If you say so...
Where did 156 come from?
Your teacher is kinda sounding like mine, pulling numbers from thin air aha
Yeah, my teacher doesn’t explain very good, and screams at the whole class if we don’t understand it the first time
First one ....this is using the Intercepting Chords Theorem
It says that.....
The measure of the angle inside the circle = (1/2)(sum of the two arcs)
So we have
(5x - 7) = (1/2)(119 + 27) multiply through by 2
2 (5x - 7) = 146 simplify
10x - 14 = 146 add 14 to both sides
10x = 160
x = 16
Note that the angle supplemental to the 78° angle is 180 - 78 = 102°
Now....we can applty the Tangent-Chord Theorem that says that
An Angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc
In simple terms :
The measure of the of the angle that measures 102° = (1/2) (23x - 3)°
So we have
102 = (1/2) (23x - 3) multiply both sides by 2
204 = 23x - 3
207 = 23x
9 = x
You may well be correct Chris but Panda told me that ALL numbers and expressions were in degrees.
See my questions #2 and her answer #3
But now that i re-read Pandas comments I can see she does not know what degrees actually are!
This never occured to me before now! Silly me!
Well it seems you must be correct. nice work Chris.
Next time I better have my mathematics forensic hat better afixed to my head!
RainbowPanda, a degree is an amount of turning.
You cannot say things like "one of the arcs and 5x-7 is another degree" That makes no sense!
You are either talking about a length (eg arc length) OR you are talking about an angle. (measured in degrees)
The 2 things are not the same at all!