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x is 20 degrees. Exterior Angle is equal to interior opposite angle. angle ART is 20, so x also becomes 20
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I meant angle SRT is 20, not ART...Typing mistake.
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The 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!
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Do NOT make assumptions, folks 😀
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In triangle PQR, angle R=180-angle P- angle Q= 180- 80-80= 20....
angle RTS is 90..
hence in triangle RTS, angle RST=180- angle R- angle RTS=189-20-90=70
angle PSQ=180-10-90=80
hence angle TSQ=180- angle PSQ- angle RST=180-70-80=30
in triangle TSO, x= 180-90-angle TSQ= 180-90-30=60
assuming intersection point is o......
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i can give you the explanation in this figure,
so by considering the middle triangle,
20+ (50-x)+ (150-x) = 180.
220-2x = 180.
40 =2x.
x=20!
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sorry, forgot to add this image
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Let 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=180-140
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.......
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By Z property angle T=70, Given PTQ angle =90, and RTQ=180 so x=180-70-90=20.......
thats all.........
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Repeat: DO NOT make assumptions, please! :😀
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X 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.
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THE SIDEs I'VE marked (SQ and SR) are equal and one common side ST and one equal angle 20. so SAS congruency...
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x is equal to 50 degree (trial and error method).
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x= 70 degree.
method: let angle TSQ= y, and angle RST= z.
therefore,
y+z=140
x+y=130
z-x=10.
and SR= SQ
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Can't find a logical way to x!
Appreciate the question anyways 😀
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The thumbnail was from previous attempts to answer. Auto-saved!
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x=30...
psq=180-spq-sqp=40------------A
angle sot(o is the intersection of sq and tp)=50---------------B
prq=20-----------------------C
in triangle pts, pst=140-------------D
THerefore, tsq=100...
Therefore, x=180-100-50=30
HENCE, X=30.
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by 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
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triangle 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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