gilded remnant
This question popped out as a multiple choice answer question during my exam, the question asked to find x + y
it was given that the options were either 50, 90, 100 or 150. I didn't get any of the answers , rather i got 140
but i seemed to misunderstand some things here since i keep getting either 130 or 140.
(the angle of x was drawn like that to ensure students wouldn't assume its 90 degrees or not)
Please help because im really curious
digital bobcatBOT
wraith cradle
Before solving this problem, i have to make sure you know some theorems, do you know this formula for finding the angle alpha?
Which Applies to this form too!
Also do you know that two parallel lines passing through a circle make two equal arcs?
also the angle looking at the arc (like shown below) is half of angle of the arc
After checking the stuff, make sure that everything i have written here is correct, then we can go on to solve this problem!
NOTE: dont worry if you dont know any of the things i sent, we can use other methods to solve it
gilded remnant
I'm only familiar with the last one the alpha and two alpha as well as the two parallel lines creating equal arcs
gilded remnant
After checking the stuff, make sure that everything i have written here is corre...
if this is based on the diagram that I've shown than I'm sorry that I forgot to mention that in the question, SOQ is a straight line
wraith cradle
I'm only familiar with the last one the alpha and two alpha as well as the two p...
Alright cool!
wraith cradle
if this is based on the diagram that I've shown than I'm sorry that I forgot to ...
Lemme re make the diagram and send it here so we can work on it
gilded remnant
alright
wraith cradle
if this is based on the diagram that I've shown than I'm sorry that I forgot to ...
this is not possible
since it would create 4 equal arcs
therefore y would be 45 degrees
Oh
It might be possible
lets see what happens
alright! Its ready
Tell me what you think of it? How did you approach this problem in the exam?
gilded remnant
Well since I knew that angle PSU was 50°, and TSU is tangent to the circle , I put the angle PRS as also 50°
and because of the parallel lines I found that y to also be 50°
wraith cradle
Yes!
gilded remnant
Its correct till that point right?
wraith cradle
Yep
gilded remnant
cuz I found myself keep getting either 50° or 40° for y
gilded remnant
Ok then, like I said PRS is 50° ,
I saw that PRS is a triangle with the line PR cross through the centre O , so I thought that PSR is 90°
wraith cradle
That is absolutely correct! ✅
gilded remnant
now I know that TSU is a tangent line as well as a straight line, I know the angle is 180, so I substract 50 and 90 from 180
Giving me a 40° on the other side
wraith cradle
Yes! And then?
gilded remnant
TRV is also a tangent line so it creates 90° angle at TRP so I substract 50° from it and get 40°
I just figured it out..
so x is basically 180 minus 40 and 40
wraith cradle
yep!
gilded remnant
x + y = 100 + 50 = 150
wraith cradle
Bro didnt need help 💀
wraith cradle
x + y = 100 + 50 = 150
Yess! ✅
gilded remnant
I swear I've gotten different answers before 😭
gilded remnant
yea lol, sorry for taking your time
wraith cradle
Nah no worries, before you close forum lemme tell you something
gilded remnant
Sure
wraith cradle
Drawing the tangents from a single point, gives you two lines that are equal
in the porblem you sent
ST = TR
therefore the triangle STR is isosceles triangle
Concluding that both angles are 40 without using any other angles to find the other angle!
gilded remnant
Oooo that's sounds quicker
wraith cradle
Yep
gilded remnant
now I'm curious is there another way to look at the question?
gilded remnant
But it's probably great to make an example if I ever needed to use those theorems
cuz I'm not taught about the first two theorems at school
wraith cradle
you probably will be, because they are very useful and also popular formulas
If you wanna solve it using the stuff i sent, you have to find the angles of the 4 arcs (which 2 of them are equal and the other 2 are equal too), you will use 50 degrees angle to show that the arc is 100 degrees, since they are parallel the other arc is 100 too!
since we know that a whole circle is 360 degrees, taking away 200 degrees leaves us with 16o degrees which we can simply conclude that each arc is 80 degrees, using the formula you should get two arcs which one of is 80 and the other is 280,
plugging the values gives us x = 280-80/2 = 100
gilded remnant
It sure seems cool that there's another to look at the question
wraith cradle
I like the way you see math! Keep it up
gilded remnant
thanks, can i add you so I can ask other problems Im unable to solve ?