Grand Quiz Question #2
The 2nd Question of the #LinkSnipped# is as follows 
Q. Using basic geometry rules, find the value of 'x' in the following figure.
[Question is worth 15 CECoins]
You shall not use trigonometry rules such as sines and cosines.
HINT: The image has not been drawn to proportion. It is advised that you draw the diagram yourself before solving.
A few instructions 
1. Your answer should be the value of x along with the approach you used to solve this problem.
We expect you to give a logical explanation of how you reached to the solution.
2. Answers with no explanation at all will be disqualified.
3. Just as we said before, the fastest to answer correctly wins!
Q. Using basic geometry rules, find the value of 'x' in the following figure.
[Question is worth 15 CECoins]
You shall not use trigonometry rules such as sines and cosines.
HINT: The image has not been drawn to proportion. It is advised that you draw the diagram yourself before solving.
A few instructions 
1. Your answer should be the value of x along with the approach you used to solve this problem.
We expect you to give a logical explanation of how you reached to the solution.
2. Answers with no explanation at all will be disqualified.
3. Just as we said before, the fastest to answer correctly wins!
Replies

Anoop Mathewx is 20 degrees. Exterior Angle is equal to interior opposite angle. angle ART is 20, so x also becomes 20

Anoop MathewI meant angle SRT is 20, not ART...Typing mistake.

PraveenKumar PurushothamanThe answer is 20 degrees. I drew it using hand and measured it. I can also be done as this way.
R = 100 = 80 + 80 + R.
P = 10.
Mid Pt = 180  60  70 = 130.
So, 150  130 = 20! 
Kaustubh KatdareDo NOT make assumptions, folks ðŸ˜€

Sagar07In triangle PQR, angle R=180angle P angle Q= 180 8080= 20....
angle RTS is 90..
hence in triangle RTS, angle RST=180 angle R angle RTS=1892090=70
angle PSQ=1801090=80
hence angle TSQ=180 angle PSQ angle RST=1807080=30
in triangle TSO, x= 18090angle TSQ= 1809030=60
assuming intersection point is o...... 
Sahithi Pallavii can give you the explanation in this figure,
so by considering the middle triangle,
20+ (50x)+ (150x) = 180.
2202x = 180.
40 =2x.
x=20! 
Sahithi Pallavisorry, forgot to add this image

bhavna guptaLet the point inside the triangle be taken as A
In triangle PQR
According to the property 1:all the sum of all the angles of a triangle is 180 or 360
therefore, P+Q+R=180
80+80+R=180
R=20
In triangle RSQ
as above property.......R+Q+S=180
20+20+S=180
S=140
Now,acc to the property 2:sum of all the angles made across the line is 180
therefore,In triangle POS...
S=180140
S=40
Again In triangle POS..
P+S+O=180
10+40+O=180
O=130
now In triangle POQ
P+Q+O=180
70+60+O=180
O=50
In triangle RST
R+S+T=180
20+140+T=180
T=20
now acc to property 2:
O in triangle SOT
130+O=180
O=50
acc to property 2:
O in triangle QOT
O=130
In triangle QOT
t=30
now acc to property 2: At T
T of triangle RST+T of triangle SOT+T of triangle QOT=180
20+T+30=180
Therefore Final answer is....T=130....... 
Sudha WaradBy Z property angle T=70, Given PTQ angle =90, and RTQ=180 so x=1807090=20.......
thats all......... 
Kaustubh KatdareRepeat: DO NOT make assumptions, please! :ðŸ˜€

CIVILPRINCESSX is 60
the triangles RST AND QST are similar... since QS=SR (OPPOSITE ANGLES ARE 20) and they have a common side ST. (SSA congruency)
i.e. RTS = STQ. => 90
X+30 = 90. => X=60. 
CIVILPRINCESS
THE SIDEs I'VE marked (SQ and SR) are equal and one common side ST and one equal angle 20. so SAS congruency... 
ultimate_kx is equal to 50 degree (trial and error method).

Guneet Khanujax= 70 degree.
method: let angle TSQ= y, and angle RST= z.
therefore,
y+z=140
x+y=130
zx=10.
and SR= SQ 
eternalthinkerCan't find a logical way to x!
Appreciate the question anyways ðŸ˜€ 
eternalthinkerThe thumbnail was from previous attempts to answer. Autosaved!

lovejeetx=30...
psq=180spqsqp=40A
angle sot(o is the intersection of sq and tp)=50B
prq=20C
in triangle pts, pst=140D
THerefore, tsq=100...
Therefore, x=18010050=30
HENCE, X=30. 
abhinaykumarby simple triangle method all angles in triangle= 180 using this equation we can solve the problem
as we all can see there are two rightangled triangles
using those we can say the angle of x is 20 
sunil paltriangle STR&STQ
ST=ST
angle SQT=angle SRT
in triangle SQR SR=SQ
so angle RST=angle TSQ
angle RSQ=140=angle RST+angle TSQ
so angle RST = angle TSQ=70
in triangle SPQ
angle PSQ=40
and angle PTQ=30
and
X+angle PTQ=90
so
X=60 ANS
X= 
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